Circulant SSA
Погребников Николай
Вспомогательные функции
library(Rssa)Предупреждение: пакет ‘Rssa’ был собран под R версии 4.2.3
Загрузка требуемого пакета: svd
Предупреждение: пакет ‘svd’ был собран под R версии 4.2.3
Загрузка требуемого пакета: forecast
Предупреждение: пакет ‘forecast’ был собран под R версии 4.2.3
Присоединяю пакет: ‘Rssa’
Следующий объект скрыт от ‘package:stats’:
decomposelibrary(signal)Предупреждение: пакет ‘signal’ был собран под R версии 4.2.3
Присоединяю пакет: ‘signal’
Следующий объект скрыт от ‘package:Rssa’:
roots
Следующие объекты скрыты от ‘package:stats’:
filter, polylibrary(gsignal)Предупреждение: пакет ‘gsignal’ был собран под R версии 4.2.3
Registered S3 methods overwritten by 'gsignal':
method from
plot.grpdelay signal
plot.specgram signal
print.freqz signal
print.grpdelay signal
print.impz signal
print.specgram signal
Присоединяю пакет: ‘gsignal’
Следующий объект скрыт ‘.GlobalEnv’:
dftmtx
Следующий объект скрыт от ‘package:signal’:
Arma, as.Arma, as.Zpg, bartlett, bilinear, blackman, boxcar, butter, buttord, cheb1ord, chebwin, cheby1, cheby2,
chirp, conv, decimate, ellip, ellipord, fftfilt, filter, filtfilt, fir1, fir2, flattopwin, freqs, freqs_plot,
freqz, freqz_plot, gausswin, grpdelay, hamming, hanning, ifft, impz, interp, kaiser, kaiserord, levinson, Ma,
medfilt1, poly, remez, resample, sftrans, sgolay, sgolayfilt, specgram, triang, unwrap, Zpg, zplane
Следующие объекты скрыты от ‘package:stats’:
filter, gaussian, polysource("eossa_new.R")
dftmtx <- function(n) {
y <- stats::mvfft(diag(1, n))
y
}
diag_averaging <- function(A){
B <- A[nrow(A):1, ] |> Re()
lapply(split(B, -(row(B) - col(B)) ), mean) |> as.numeric()
}
shift_vector <- function(vec) {
last_element <- tail(vec, 1)
vec <- vec[-length(vec)]
shifted_vec <- c(last_element, vec)
return(shifted_vec)
}
extend <- function(x, H){
# Вычисление коэффициентов AR модели для дифференцированного ряда
N <- length(x)
p <- floor(N / 3)
dx <- diff(x)
# A <- ar(dx, order.max = p, method = "yule-walker")$ar
A <- aryule(dx, p)$a
# Правое расширение
y <- x
dy <- diff(y)
er <- signal::filter(A, 1, dy)
dy <- signal::filter(1, A, c(er, rep(0, H)))
y <- y[1] + c(0, cumsum(dy))
# Левое расширение
y <- rev(y)
dy <- diff(y)
er <- signal::filter(A,1,dy)
dy <- signal::filter(1,A,c(er, rep(0, H)))
y <- y[1] + c(0, cumsum(dy))
# Расширенный ряд
xe <- rev(y)
# Вывод результатов
xe
}CiSSA
Подаётся на вход временной ряд, длина окна (если её нет, то она равна длине ряда + 1 пополам) и информация о том, нужно ли расширить ряд. Расширять ряд стоит при стохастическом тренде (Autoregressive extension (default). It is indicated for stationary and stochastic trend time series as well). Реализовано только Autoregressive extension.
На выходе список выдаётся список list(t_series, importance).
t_series — матрица, по столбцам которой располагаются временные ряды,
отвечающие за частоты (i-1)/L, где i — номер столбца, L — длина
окна.
importance — вектор, отвечающий за значимость i-ого временного ряда в
разлолжении. Чем больше значение, тем больший вклад внёс i-тый временной
ряд.
circulant_SSA <- function(ts, L = NULL, extend_flag = FALSE){
time_series <- ts
# Construct trajectory matrix
N <- length(time_series)
if (is.null(L)){
L <- (N + 1)%/%2
}
# Проверка на расширения ряда
if (extend_flag == FALSE){
H <- 0
time_series <- ts
}
else{
H <- L
time_series <- extend(ts, H)
}
X <- hankel(time_series, L)
# Number of symmetric frequency pairs around 1/2
if (L %% 2) {
nf2 <- (L + 1) / 2 - 1
} else {
nf2 <- L / 2 - 1
}
# Number of frequencies <= 1/2
nft <- nf2 + abs((L %% 2) - 2)
# Decomposition
# Estimate autocovariance OK
autocov <- numeric(L)
for (m in 0:(L-1)){
autocov[[m+1]] <- sum(time_series[1:(N-m)] * time_series[(1+m):N]) / (N-m)
}
# First row of circulant matrix
circ_first_row <- numeric(L)
for (m in 0:(L-1)){
circ_first_row[[m+1]] <- (L-m)/L * autocov[[m+1]] + (m)/L * autocov[[L-m]]
}
# Build circulant matrix
S_C <- matrix(circ_first_row, nrow = 1)
shifted_vector <- circ_first_row
for (i in 2:(L)) {
shifted_vector <- shift_vector(shifted_vector)
# S_C <- rbind(S_C, as.vector(shifted_vector))
S_C <- rbind(as.vector(shifted_vector), S_C)
}
# Eigenvectors of circulant matrix (unitary base)
U <- dftmtx(L)/sqrt(L)
# Real eigenvectors (orthonormal base)
U[, 1] <- Re(U[, 1])
for (k in 1:nf2) {
u_k <- U[, k + 1]
U[, k + 1] <- sqrt(2) * Re(u_k)
U[, L + 2 - (k + 1)] <- sqrt(2) * Im(u_k)
}
if (L %% 2 != 0) {
U[, nft] <- Re(U[, nft])
}
# Eigenvalues of circulant matrix: estimated power spectral density
psd <- abs(diag(t(U) %*% S_C %*% U))
# Principal components
W <- t(U) %*% X
# Reconstruction
# Elementary reconstructed series
R <- matrix(0, nrow = N+2*H, ncol = L)
for (k in 1:L) {
R[, k] <- U[ ,k] %*% t(W[k, ]) |> diag_averaging()
}
# Grouping by frequency
# Elementary reconstructed series by frequency
Z <- matrix(0, nrow = N+2*H, ncol = nft)
Z[, 1] <- R[, 1]
# Importance of component
imp <- numeric(nft)
lambda_sm <- sum(psd)
imp[1] <- psd[1]/lambda_sm
for (k in 1:nf2) {
Z[, k + 1] <- R[, k + 1] + R[, L + 2 - (k + 1)]
imp[k+1] <- (psd[k+1] + psd[ L + 2 - (k + 1)])/lambda_sm
}
if (L %% 2 != 0) {
Z[, nft] <- R[, nft]
imp[nft] <- psd[nft] / lambda_sm
}
list(t_series = Z[(H+1):(N+H),],
importance = imp,
freq = (0:(length(imp) -1))/L
)
}# groups - list of frequencies
grouping_cissa <- function(cissa_res, groups){
freq <- cissa_res$freq
t_series <- cissa_res$t_series
residuals <- 0
result <- setNames(as.list(rep(0, length(groups))), names(groups))
for (i in 1:length(cissa_res$freq)){
flag <- FALSE
for (name in names(groups)){
if (groups[[name]][1] <= freq[i] & freq[i] <= groups[[name]][2]){
flag <- TRUE
result[[name]] <- result[[name]] + t_series[, i]
}
}
if (flag == FALSE){
residuals <- residuals + t_series[, i]
}
}
result[["residuals"]] <- residuals
result
}generate_ts <- function(func, n=1e3, ...){
1:n |> func(...) |> ts()
}
f_cos <- function(x, A = 1, omega = 1/4, phi = 0){
f_exp_mod_harm_series(x, A, alpha = 0, omega = omega, phi = phi)
}
f_sin <- function(x, A = 1, omega = 1/4, phi = 3*pi/2){
f_exp_mod_harm_series(x, A, alpha = 0, omega = omega, phi = phi)
}
f_exp <- function(x, A = 1, alpha = 1){
A * exp(alpha * x)
}
f_exp_cos <- function(x, A = 1, alpha = 1, omega = 1/4, phi = 0){
f_exp_mod_harm_series(x, A, alpha, omega, phi)
}
f_const <- function(x, C = 0){
rep(C, length(x))
}
f_exp_mod_harm_series <- function(x, A = 1, alpha = 1, omega = 1/4, phi = 0){
A*exp(alpha*x)*cos(2*pi*omega*x + phi)
}
f_linear <- function(x, a = 1, b = 0){
a*x + b
}
mse <- function(f_true, f_reconstructed){
mean((f_true - f_reconstructed)^2)
}Ошибка при Lw in N, Kw not in N
n <- 96*2+5
L <- 96
f_sum <- function(x){
f_const(x, C = 1) + f_cos(x, omega = 1/12)
}
f_const |> generate_ts(n, C = 1) |>
plot(col = "green", ylim = c(-1, 2), ylab = "f_n")
f_cos |>
generate_ts(n, omega = 1/12) |>
lines(col="green")f_sum |> generate_ts(n) |> lines(lwd = 3, col='red')
f_n <- f_sum(1:n)
c <- circulant_SSA(f_n, L = 96, extend_flag = FALSE)
r <- grouping_cissa(c,
groups = list(
trend = c(0, 1/100),
sesonal = c(1/99, 1/10)
)
)
f_C <- f_const |> generate_ts(n, C = 1)
f_c <- f_cos |> generate_ts(n, omega = 1/12)
print("Ошибки при CiSSA")[1] "Ошибки при CiSSA"print(paste("Ошибка при вычислении C = 1: ", mse(f_C, r$trend) |> format(scientific = TRUE, digits = 2) ))[1] "Ошибка при вычислении C = 1: 3.2e-31"print(paste("Ошибка при вычислении cos(pi/12): ", mse(f_c, r$sesonal) |> format(scientific = TRUE, digits = 2) ))[1] "Ошибка при вычислении cos(pi/12): 3.6e-30"lines(1:n, r$trend, col="blue")lines(1:n, r$sesonal, col="blue")
f_const |> generate_ts(n, C = 1) |>
plot(col = "green", ylim = c(-1, 2), ylab = "f_n")
f_cos |>
generate_ts(n, omega = 1/12) |>
lines(col="green")f_sum |> generate_ts(n) |> lines(lwd = 3, col='red')
f_n <- f_sum(1:n)
s <- ssa(f_n, L = 96)
r <- reconstruct(s, groups=list(
trend = 1,
sesonal = 2:3
))
print("Ошибки при SSA")[1] "Ошибки при SSA"print(paste("Ошибка при вычислении C = 1: ", mse(f_C, r$trend) |> format(scientific = TRUE, digits = 2) ))[1] "Ошибка при вычислении C = 1: 9.6e-05"print(paste("Ошибка при вычислении cos(pi/12): ", mse(f_c, r$sesonal) |> format(scientific = TRUE, digits = 2)))[1] "Ошибка при вычислении cos(pi/12): 9.6e-05"lines(1:n, r$trend)lines(1:n, r$sesonal)
Проверка разделимости непериодических компонент + автогруппировка SSA
n <- 96*2-1
L <- 96
C <- 1
omega_cs <- 1/12
omega_sn <- 1/24
a <- 1/100
f_sum <- function(x){
f_const(x, C = C) +
f_cos(x, omega = omega_cs) +
f_exp(x, a = a) +
f_sin(x, omega = omega_sn)
}
f_C <- f_const |> generate_ts(n, C = C)
f_c <- f_cos |> generate_ts(n, omega = omega_cs)
f_s <- f_sin |> generate_ts(n, omega = omega_sn)
f_e <- f_exp |> generate_ts(n, a = a)
f_n <- f_sum(1:n)
library(xtable)Предупреждение: пакет ‘xtable’ был собран под R версии 4.2.3# Шаг 2: Создание примера данных
data <- data.frame(
Метод = c("SSA", "CiSSA"),
e_err = c(20, 20),
c_err = c(23, 35),
ec_err = c(20, 20),
sin_err = c (20, 20),
cos_err = c(1, 1)
)
# Отрисовка ряда f_n
plot(f_n, type = "l", lwd = 3, col = 'red', ylim = c(-2, 10),
xlab = "Время", ylab = "Значения ряда", main = "Разложение временного ряда")
# Добавление отдельных компонентов (f_C, f_c, f_e)
lines(f_C, col = "blue") # Компонент f_Clines(f_c, col = "blue") # Компонент f_c
lines(f_e, col = "blue") # Компонент f_elines(f_s, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
c <- circulant_SSA(f_n, L = L, extend_flag = TRUE)
# r <- c$t_series
r <- grouping_cissa(c,
groups = list(
# trend = c(0, 1/100),
trend = c(0, 1/1000),
sesonal_cos = c(1/14, 1/10),
sesonal_sin = c(1/26, 1/23)
))
data$cos_err[2] <- mse(f_s, r$sesonal_sin) |> formatC(format = "e", digits = 1)
data$sin_err[2] <- mse(f_c, r$sesonal_cos) |> formatC(format = "e", digits = 1)
data$ec_err[2] <- mse(f_C+f_e, r$trend) |> formatC(format = "e", digits = 1)
# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/CiSSA.png") # сохранение в формате PNG
plot(1:n, f_n, type = "l", lwd=3, ylim= c(-2, 10), col="red",
xlab = "Время", ylab = "Значения ряда", main = "CiSSA разложение временного ряда")
lines(1:n, r$trend, col = "blue")lines(1:n, r$sesonal_sin, col = "blue")
lines(1:n, r$sesonal_cos, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
# dev.off() # завершение сохранения
s <- ssa(f_n, L)
e <- eossa(s, 1:10, k = 7)
g_sesonal <- grouping.auto(e, base = "eigen",
freq.bins = list(trend = c(0.001),
sesonal2 = c(1/25, 1/23),
sesonal1 = c(1/13, 1/11)
),
threshold = 0.1)
r <- Rssa::reconstruct(e, groups=c(list(exp = 1,
C = 2
),
g_sesonal)
)
plot(wcor(e, groups = 1:24), scales = list(at = c(10, 20, 30)))Предупреждение в wcor.ossa(e, groups = 1:24) :
Component matrices are not F-orthogonal (max F-cor is 0.93). W-cor matrix can be irrelevant
data$c_err[1] <- mse(f_C, r$C) |> formatC(format = "e", digits = 1)
data$e_err[1] <- mse(f_e, r$exp) |> formatC(format = "e", digits = 1)
data$cos_err[1] <- mse(f_c, r$sesonal1) |> formatC(format = "e", digits = 1)
data$sin_err[1] <- mse(f_s, r$sesonal2) |> formatC(format = "e", digits = 1)
data$ec_err[1] <- mse(f_C+f_e, r$C+r$exp) |> formatC(format = "e", digits = 1)
# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/SSA.png") # сохранение в формате PNG
plot(1:n, f_n, type = "l", lwd=3, ylim= c(-2, 10), col="red",
xlab = "Время", ylab = "Значения ряда", main = "SSA разложение временного ряда")
lines(1:n, r$trend, type = "l", col="green")lines(1:n, r$exp, type = "l", ylim= c(-2, 10), col="blue")
lines(1:n, r$C, col = "blue")lines(1:n, r$sesonal1, col = "blue")
lines(1:n, r$sesonal2, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
# Шаг 3: Преобразование данных в формат LaTeX
table_latex <- xtable(data, caption = "Example Table")
# Шаг 4: Вывод таблицы в LaTeX файл
print(table_latex, include.rownames = FALSE)% latex table generated in R 4.2.2 by xtable 1.8-4 package
% Mon Nov 4 13:25:09 2024
\begin{table}[ht]
\centering
\begin{tabular}{llllll}
\hline
Метод & e\_err & c\_err & ec\_err & sin\_err & cos\_err \\
\hline
SSA & 2.2e-25 & 2.2e-25 & 4.2e-28 & 3.8e-29 & 1.6e-29 \\
CiSSA & 20 & 35 & 3.5e-02 & 1.4e-04 & 1.9e-03 \\
\hline
\end{tabular}
\caption{Example Table}
\end{table}Пример cos*exp
n <- 96*2-1
L <- 96
eps <- 1/(L+1)
C <- 1
omega_cs <- 1/12
omega_sn <- 1/24
a <- 1/100
omega_exp <- 1/48
f_sum <- function(x){
f_cos(x, omega = omega_cs) +
f_exp_mod_harm_series(x, a = a, omega = omega_exp) +
f_sin(x, omega = omega_sn)
}
f_c <- f_cos |> generate_ts(n, omega = omega_cs)
f_s <- f_sin |> generate_ts(n, omega = omega_sn)
f_e <- f_exp_mod_harm_series |> generate_ts(n, a = a, omega = omega_exp)
f_n <- f_sum(1:n)
library(xtable)
# Шаг 2: Создание примера данных
data <- data.frame(
Метод = c("SSA", "CiSSA"),
exp_err = c(20, 20),
sin_err = c (20, 20),
cos_err = c(1, 1)
)
# Отрисовка ряда f_n
plot(f_n, type = "l", lwd = 3, col = 'red', ylim = c(-10, 10),
xlab = "Время", ylab = "Значения ряда", main = "Разложение временного ряда")
# Добавление отдельных компонентов (f_C, f_c, f_e)
lines(f_c, col = "blue") # Компонент f_clines(f_e, col = "blue") # Компонент f_e
lines(f_s, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
c <- circulant_SSA(f_n, L = L, extend_flag = TRUE)
# r <- c$t_series
r <- grouping_cissa(c,
groups = list(
trend = c(0, 1/26-eps),
sesonal_cos = c(1/14, 1/10),
sesonal_sin = c(1/26, 1/23)
))
data$cos_err[2] <- mse(f_s, r$sesonal_sin) |> formatC(format = "e", digits = 1)
data$sin_err[2] <- mse(f_c, r$sesonal_cos) |> formatC(format = "e", digits = 1)
data$exp_err[2] <- mse(f_e, r$trend) |> formatC(format = "e", digits = 1)
# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/CiSSA.png") # сохранение в формате PNG
plot(1:n, f_n, type = "l", lwd=3, ylim= c(-10, 10), col="red",
xlab = "Время", ylab = "Значения ряда", main = "CiSSA разложение временного ряда")
lines(1:n, r$trend, col = "blue")lines(1:n, r$sesonal_sin, col = "blue")
lines(1:n, r$sesonal_cos, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
# dev.off() # завершение сохранения
s <- ssa(f_n, L)
e <- eossa_new(s, nested.groups = list(1:30), clust_type = "distance")
g_sesonal <- grouping.auto(e, base = "eigen",
freq.bins = list(trend = c(1/25-eps),
sesonal2 = c(1/25, 1/23),
sesonal1 = c(1/13, 1/11)
),
threshold = 0.1)
r <- reconstruct(e, groups= g_sesonal)
plot(wcor(e, groups = 1:24), scales = list(at = c(10, 20, 30)))Предупреждение в wcor.ossa(e, groups = 1:24) :
Component matrices are not F-orthogonal (max F-cor is -0.529). W-cor matrix can be irrelevant
data$exp_err[1] <- mse(f_e, r$trend) |> formatC(format = "e", digits = 1)
data$cos_err[1] <- mse(f_c, r$sesonal1) |> formatC(format = "e", digits = 1)
data$sin_err[1] <- mse(f_s, r$sesonal2) |> formatC(format = "e", digits = 1)
# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/SSA.png") # сохранение в формате PNG
plot(1:n, f_n, type = "l", lwd=3, ylim= c(-10, 10), col="red",
xlab = "Время", ylab = "Значения ряда", main = "SSA разложение временного ряда")
lines(1:n, r$trend, type = "l", col="blue")lines(1:n, r$sesonal1, col = "blue")
lines(1:n, r$sesonal2, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
# Шаг 3: Преобразование данных в формат LaTeX
table_latex <- xtable(data, caption = "Example Table")
# Шаг 4: Вывод таблицы в LaTeX файл
print(table_latex, include.rownames = FALSE)% latex table generated in R 4.2.2 by xtable 1.8-4 package
% Mon Nov 4 13:25:10 2024
\begin{table}[ht]
\centering
\begin{tabular}{llll}
\hline
Метод & exp\_err & sin\_err & cos\_err \\
\hline
SSA & 4.7e-29 & 1.1e-29 & 8.4e-30 \\
CiSSA & 3.2e-02 & 2.6e-04 & 5.8e-03 \\
\hline
\end{tabular}
\caption{Example Table}
\end{table}Данные IP
library(readxl)Предупреждение: пакет ‘readxl’ был собран под R версии 4.2.3data <- read_excel("Data/International_Financial_Statistics_.xlsx")New names:
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• `` -> `...579`data |> head()Отрисовка данных IP
dates <- seq(as.Date("1970-01-01"), as.Date("2018-1-30"), by = "month")
IP_values <- data[2, -c(1, 2)] |> as.double()
plot(dates, IP_values, type="l")
Cissa
Отрисовка трендовой составляющей чёрным цветом, основной временной ряд — красным
data_slice <- 1:537
dates_slice <- dates[data_slice]
IP_values_slice <- IP_values[data_slice]
eps <- 1/193
c <- circulant_SSA(IP_values_slice, L = 192, extend_flag = TRUE)
r <- c$t_series
r <- grouping_cissa(c,
groups = list(
trend = c(0, 1/192),
cycle = c(1/97, 5/95),
sesonal = c(1/13, 1/2+0.0001)
)
)
r_sesonal <- grouping_cissa(c,
groups = list(
s1 = c(16/192 - eps, 16/192 + eps),
s2 = c(32/192 - eps, 32/192 + eps),
s3 = c(48/192 - eps, 48/192 + eps),
s4 = c(64/192 - eps, 64/192 + eps),
s5 = c(80/192 - eps, 80/192 + eps),
s6 = c(96/192 - eps, 96/192 + eps)
)
)
# cissa_trend <- r[,1] + r[,2]
# cissa_cycle <- r[, 3:11] |> rowSums()
# cissa_sesonal <- r[, c(17, 33, 49, 65, 81, 97)] |> rowSums()
# cissa_residuals <- IP_values_slice - (cissa_trend + cissa_cycle + cissa_sesonal)
cissa_trend <- r$trend
cissa_cycle <- r$cycle
cissa_sesonal <- Reduce("+", r_sesonal |> within(rm(residuals)))
cissa_residuals <- IP_values_slice - (cissa_trend + cissa_cycle + cissa_sesonal)
plot(dates_slice, IP_values_slice,
type="l", col = "black")
lines(dates_slice, cissa_trend,
type="l", col = "red")
plot(dates_slice, cissa_cycle,
type="l", col = "red")
plot(dates_slice, cissa_sesonal,
type="l", col = "red")
plot(dates_slice, cissa_residuals,
type="l", col = "red")
plot(dates_slice, IP_values_slice,
type="l", col = "black")
lines(dates_slice, cissa_trend+cissa_cycle+cissa_sesonal,
type="l", col = "red")
SSA fossa
s <- ssa(IP_values_slice, L = 192)
e <- fossa(s)
# e <- eossa_new(s, nested.groups = list(1:30), clust_type = "distance")
eps <- 1/193
groups <- grouping.auto(e,
freq.bins = list(trend = c(1/192),
cycle = c(1/97, 5/95),
s1 = c(16/192 - eps, 16/192 + eps),
s2 = c(32/192 - eps, 32/192 + eps),
s3 = c(48/192 - eps, 48/192 + eps),
s4 = c(64/192 - eps, 64/192 + eps),
s5 = c(80/192 - eps, 80/192 + eps),
s6 = c(96/192 - eps, 96/192 + eps)
),
threshold = 0)
plot(wcor(e, groups = 1:30), scales = list(at = c(10, 20, 30)),
main = "W-correlation matrix SSA (fossa)")
r <- reconstruct(e, groups=groups)
ssa_trend_f <- r$trend
ssa_cycle_f <- r$cycle
ssa_sesonal_f <- r$s1 + r$s2 + r$s3 + r$s4 + r$s5 + r$s6
ssa_residuals_f <- IP_values_slice - (ssa_trend_f + ssa_cycle_f + ssa_sesonal_f)
plot(dates_slice, IP_values_slice,
type="l", col = "black")
lines(dates_slice, ssa_trend_f,
type="l", col = "magenta")
plot(dates_slice, ssa_cycle_f,
type="l", col = "magenta")
plot(dates_slice, ssa_sesonal_f,
type="l", col = "magenta")
plot(dates_slice, ssa_residuals_f,
type="l", col = "magenta")
SSA eossa
library(Rssa)
source("eossa_new.r")
s <- ssa(IP_values_slice, L = 192)
e <- eossa_new(s, nested.groups = list(1:30), clust_type = "distance")
groups <- grouping.auto(e,
freq.bins = list(trend = c(1/192),
cycle = c(1/97, 5/95),
s1 = c(16/192 - eps, 16/192 + eps),
s2 = c(32/192 - eps, 32/192 + eps),
s3 = c(48/192 - eps, 48/192 + eps),
s4 = c(64/192 - eps, 64/192 + eps),
s5 = c(80/192 - eps, 80/192 + eps),
s6 = c(96/192 - eps, 96/192 + eps)
),
threshold = 0)
plot(wcor(e, groups = 1:30), scales = list(at = c(10, 20, 30)),
main = "W-correlation matrix SSA (eossa)")Предупреждение в wcor.ossa(e, groups = 1:30) :
Component matrices are not F-orthogonal (max F-cor is -0.0621). W-cor matrix can be irrelevant
r <- reconstruct(e, groups=groups)
ssa_trend <- r$trend
ssa_cycle <- r$cycle
ssa_sesonal <- r$s1 + r$s2 + r$s3 + r$s4 + r$s5 + r$s6
ssa_residuals <- IP_values_slice - (ssa_trend + ssa_cycle + ssa_sesonal)
plot(dates_slice, IP_values_slice,
type="l", col = "black")
lines(dates_slice, ssa_trend,
type="l", col = "blue")
plot(dates_slice, ssa_cycle,
type="l", col = "blue")
plot(dates_slice, ssa_sesonal,
type="l", col = "blue")
plot(dates_slice, ssa_residuals,
type="l", col = "blue")
plot(dates_slice, IP_values_slice,
main = "IP USA тренд",xlab = "Время", ylab = "Значение",
type="l", col = "black")
lines(dates_slice, ssa_trend,
type="l", col = "blue", lwd=2)lines(dates_slice, ssa_trend_f,
type="l", col = "magenta", lwd=2)
lines(dates_slice, cissa_trend,
type="l", col = "red", lwd=2)# Легенда
legend("topleft", legend = c("Весь ряд", "CiSSA тренд", "SSA тренд (eossa)", "SSA тренд (fossa)"),
col = c("black", "red", "blue", "magenta"), lty = 1, lwd = 3)
plot(dates_slice, ssa_cycle,
main = "IP USA цикличность", xlab = "Время", ylab = "Значение",
type="l", col = "blue", ylim=c(-10, 10), lwd=2)
lines(dates_slice, cissa_cycle,
type="l", col = "red", lwd=2)lines(dates_slice, ssa_cycle_f,
type="l", col = "magenta", lwd=2)
# Легенда
legend("topleft", legend = c("CiSSA", "SSA (eossa)", "SSA (fossa)"),
col = c("red", "blue", "magenta"), lty = 1, lwd = 3)
# Настройка графиков для отображения двух графиков один под другим с общей осью X
layout(matrix(c(1, 2), nrow = 2, byrow = TRUE), heights = c(1, 1.2))
# Построение первого графика
par(mar = c(2, 4, 2, 2)) # Уменьшение нижнего отступа
plot(dates_slice, ssa_sesonal, type = "l", col = "blue", lwd = 1,
main = "SSA (eossa) сезонность", xlab = "", ylab = "Значение")
# Добавление оси X внизу первого графика, но с пустыми метками
axis(1, labels = FALSE)
# Построение второго графика
par(mar = c(5, 4, 2, 2)) # Увеличение нижнего отступа
plot(dates_slice, ssa_sesonal_f, type = "l", col = "magenta", lwd = 1,
main = "SSA (fossa) сезонность", xlab = "Время", ylab = "Значение")
par(mar = c(3, 4, 2, 2)) # Увеличение нижнего отступа
plot(dates_slice, cissa_sesonal, type = "l", col = "red", lwd = 1,
main = "CiSSA сезонность", xlab = "Время", ylab = "Значение")
# Восстановление макета по умолчанию
layout(1)
NA
NAplot(dates_slice, ssa_residuals,
main = "IP USA остаток", xlab = "Время", ylab = "Значение",
type="l", col = "blue", ylim=c(-2, 2))
lines(dates_slice, cissa_residuals,
type="l", col = "red")lines(dates_slice, ssa_residuals_f,
type="l", col = "magenta")
legend("topleft", legend = c("CiSSA", "SSA (eossa)", "SSA (fossa)"),
col = c("red", "blue", "magenta"), lty = 1, lwd = 3)
ssa_residuals |> density() |> plot()
cissa_residuals |> density() |> plot()
Отделение сигнала от шума
set.seed(100)
n_mse_tests <- function(n){
n <- 96*2-1
L <- 96
sigma <- 0.1
C <- 1
omega_cs <- 1/12
omega_sn <- 1/24
a <- 1/100
f_sum <- function(x){
f_const(x, C = C) +
f_cos(x, omega = omega_cs) +
f_exp(x, a = a) +
f_sin(x, omega = omega_sn)
}
f_C <- f_const |> generate_ts(n, C = C)
f_c <- f_cos |> generate_ts(n, omega = omega_cs)
f_s <- f_sin |> generate_ts(n, omega = omega_sn)
f_e <- f_exp |> generate_ts(n, a = a)
mse_lst <- list()
for (i in 1:n) {
f_noise <- rnorm(n, sd = sigma)
f_n <- f_sum(1:n) + f_noise
c <- circulant_SSA(f_n, L = L, extend_flag = TRUE)
# r <- c$t_series
r <- grouping_cissa(c, groups= list(trend = c(0, 1/1000),
sesonal2 = c(1/25, 1/23),
sesonal1 = c(1/13, 1/10)
))
# mse_lst$cissa <- c(mse_lst$cissa, mse(f_sum(1:n), r[, 9] + r[, 5] + r[, 1]))
mse_lst$cissa <- c(mse_lst$cissa,
mse(f_sum(1:n),
r$trend + r$sesonal1 + r$sesonal2))
s <- ssa(f_n, L)
# e <- eossa(s, 1:10, k = 6)
e <- fossa(s)
g_sesonal <- grouping.auto(e, base = "eigen",
freq.bins = list(trend = 1/1000,
sesonal2 = c(1/25, 1/23),
sesonal1 = c(1/13, 1/10)
),
threshold = 0.5)
r <- reconstruct(e, groups=c(list(exp = 1, C = 2), g_sesonal))
mse_lst$ssa <-
c(mse_lst$ssa, mse(f_sum(1:n), r$trend + r$sesonal2 + r$sesonal1))
}
return(mse_lst)
}
res_mse_test <- n_mse_tests(10000)
# Оценка плотности
density_estimate_cissa <- density(res_mse_test$cissa)
# Построение графика плотности
plot(density_estimate_cissa, main = "Оценка плотности",
xlab = "Значение", ylab = "Плотность",
col = "blue", lwd = 2)
density_estimate_ssa <- density(res_mse_test$ssa)
# Построение графика плотности
plot(density_estimate_ssa, main = "Оценка плотности",
xlab = "Значение", ylab = "Плотность",
col = "blue", lwd = 2)
res_mse_test$cissa |> summary() Min. 1st Qu. Median Mean 3rd Qu. Max.
0.02299 0.03062 0.03345 0.03378 0.03575 0.04800 res_mse_test$cissa |> sd()[1] 0.004333975res_mse_test$ssa |> summary() Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000576 0.001710 0.002125 0.002228 0.002585 0.006311 res_mse_test$ssa |> sd()[1] 0.0008283841Как выполняется расширение ряда
IP_values_slice |> extend(192) |> plot(type="l", lwd = 3)
c(rep(0, 192),IP_values_slice) |> lines(type="l", col="red")
Фурье преобразование
n <- 96*2
L <- 96
x <- 0:(n-1)
y1 <- cos(2 * pi / 12 * x) # Первая компонента
y2 <- sin(2 * pi / 48 * x) # Вторая компонента
# Создаем общий временной ряд
y <- y1 + y2
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
# Индексы для частот
n <- length(y)
frequencies <- (0:(n-1)) / n
# Функция для восстановления компонент
reconstruct_fft <- function(frequencies, amplitudes, phases) {
reconstructed <- list()
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
reconstructed[[i]] <-
amplitudes[i] * cos(2 * pi * frequencies[i] * x + phases[i]) / n * 2
}
return(reconstructed)
}
# y_main <- y
# X <- hankel(y)
# K <- dim(X)[2]
# res <- list()
# for (i in 1:K){
# y <- X[, i]
#
# # Выполняем быстрое преобразование Фурье
# fft_y <- fft(y)
#
# # Получаем амплитуды и фазы
# amplitudes <- Mod(fft_y)
# phases <- Arg(fft_y)
#
# res[[i]] <- reconstruct_fft(frequencies, amplitudes, phases)
# }
#
# nft <- res[[1]]
# print(nft |> length())
# res_full <- matrix(0, nrow = |> length(), )
#
# for (i in 1:K){
# res_full <-
# }
#
#
y_reconstructed <- reconstruct_fft(frequencies, amplitudes, phases)
# Строим графики
for (i in 1:(n)){
plot(x, y_reconstructed[[i]], main = paste(frequencies[i]))
}
plot(x, Reduce("+", y_reconstructed), type = "l")
# lines(x, y, col = "red", type = "l", lty = 2)x <- 1:100
y <- sin(2*pi*x)
dftmtx(10)[3, 2][1] 0.309017-0.9510565idftmtx(10)[2, 3][1] 0.309017-0.9510565i(as.matrix(dftmtx(10)[3, ])) %*% t(as.matrix(Conj(dftmtx(10)[, 3]))) [,1] [,2] [,3] [,4] [,5]
[1,] 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i
[2,] 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i
[3,] -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i
[4,] -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000-0.0000000i 0.309017+0.9510565i
[5,] 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i
[6,] 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i
[7,] 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i
[8,] -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i
[9,] -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000-0.0000000i 0.309017+0.9510565i
[10,] 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i
[,6] [,7] [,8] [,9] [,10]
[1,] 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i
[2,] 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i
[3,] -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i
[4,] -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i
[5,] 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i
[6,] 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i
[7,] 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i
[8,] -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i
[9,] -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i
[10,] 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000idim( t(as.matrix(Conj(dftmtx(10)[3, ]))))[1] 1 10dim(as.matrix(dftmtx(10)[3, ]))[1] 10 1
X <- matrix(c(32, 21, 23,
521,631452, 25251,
1536, 75, 38), nrow= 3)
f_mat <- dftmtx(3) / sqrt(3)
f_mat_inv <- Conj(f_mat)
X [,1] [,2] [,3]
[1,] 32 521 1536
[2,] 21 631452 75
[3,] 23 25251 38f_mat %*% f_mat_inv %*% X [,1] [,2] [,3]
[1,] 32+0i 521+0i 1536+0i
[2,] 21+0i 631452+0i 75+0i
[3,] 23+0i 25251+0i 38+0idata_slice <- 1:538
n <- 96*2
L <- 96
x <- data_slice
y1 <- cos(2 * pi / 12 * x) # Первая компонента
y2 <- sin(2 * pi / 48 * x) # Вторая компонента
# Создаем общий временной ряд
y <- IP_values[data_slice]
y_extended <- y |> extend(L)
x <- 1:length(y_extended)
y <- IP_values[data_slice]
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
# Индексы для частот
n <- length(y)
frequencies <- (0:(n-1)) / n
# Функция для восстановления компонент
reconstruct_fft <- function(frequencies, amplitudes, phases) {
reconstructed <- list()
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
reconstructed[[i]] <-
amplitudes[i] * cos(2 * pi * frequencies[i] * x + phases[i]) / n * 2
}
return(reconstructed)
}
y_reconstructed <- reconstruct_fft(frequencies, amplitudes, phases)
# Строим графики
for (i in 1:(n)){
plot(x, y_reconstructed[[i]], main = paste(frequencies[i]))
}
data_slice <- 1:538
n <- 96*2
L <- 96
x <- data_slice
y1 <- cos(2 * pi / 12 * x) # Первая компонента
y2 <- sin(2 * pi / 48 * x) # Вторая компонента
# Создаем общий временной ряд
y <- IP_values[data_slice]
y_extended <- y |> extend(L)
x <- 1:length(y_extended)
y <- IP_values[data_slice]
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
# Индексы для частот
n <- length(y)
frequencies <- (0:(n-1)) / n
# Функция для восстановления компонент
reconstruct_fft <- function(frequencies, amplitudes, phases) {
reconstructed <- list()
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
reconstructed[[i]] <-
amplitudes[i] * cos(2 * pi * frequencies[i] * x + phases[i]) / n * 2
}
return(reconstructed)
}
y_reconstructed <- reconstruct_fft(frequencies, amplitudes, phases)
# Строим графики
for (i in 1:(n)){
plot(x, y_reconstructed[[i]], main = paste(frequencies[i]))
}
n <- 96*2-1
x <- 0:(n-1)
L <- 96
y <- sin(2*pi/12 * x)
X <- hankel(y, L)
Ft <- dftmtx(L) / sqrt(L)
Ft_inv <- t(Conj(Ft))
component_wise_mult <- function(index){
Ft %*% t(sweep(Ft_inv, 1, X[, index], '*'))
}
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, nrow = n, ncol = L)
for (i in 1:K){
res[i:(i+L-1), ] <- res[i:(i+L-1), ] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[i, ] <- res[i, ] / counters[i]
}
res
}
res_comp_wise <- lapply(1:L, component_wise_mult)
print(res_comp_wise[[1]]) [,1] [,2] [,3] [,4] [,5]
[1,] 0+0i 1.387779e-17-4.374756e-17i 2.255141e-17+1.778092e-17i -1.561251e-17+1.994932e-17i -5.377643e-17-6.505213e-18i
[2,] 0+0i 5.000000e-01+0.000000e+00i 6.938894e-18-6.776264e-17i 1.561251e-17-6.418477e-17i -6.938894e-18+1.170938e-17i
[3,] 0+0i 1.040834e-17-2.569559e-17i 8.660254e-01+0.000000e+00i -3.989864e-17-3.165870e-17i -5.898060e-17-3.361027e-17i
[4,] 0+0i -2.949030e-17+2.634611e-17i 6.938894e-17-2.667137e-17i 1.000000e+00-0.000000e+00i 2.949030e-17-1.994932e-17i
[5,] 0+0i 5.204170e-18-4.987330e-18i -1.734723e-17-2.602085e-18i 2.949030e-17+0.000000e+00i 8.660254e-01-0.000000e+00i
[6,] 0+0i 5.204170e-18+6.505213e-18i 0.000000e+00-3.187554e-17i -5.377643e-17-1.431147e-17i -3.469447e-18+1.144917e-16i
[7,] 0+0i 3.469447e-18-4.770490e-18i -2.775558e-17-4.336809e-19i -3.469447e-18-6.071532e-18i 2.255141e-17-2.168404e-18i
[8,] 0+0i -1.734723e-18+1.647987e-17i 0.000000e+00-8.673617e-18i -1.144917e-16+1.149254e-16i -6.938894e-18-1.214306e-17i
[9,] 0+0i 0.000000e+00+6.071532e-18i 1.734723e-18-5.637851e-18i 0.000000e+00+1.734723e-18i 5.204170e-17-1.301043e-17i
[10,] 0+0i -8.673617e-19-4.336809e-19i -5.204170e-18-5.204170e-18i 2.949030e-17+5.204170e-18i 1.040834e-17+3.469447e-18i
[,6] [,7] [,8] [,9]
[1,] 0.000000e+00+4.987330e-18i 5.777790e-34-3.274081e-33i -3.469447e-18+7.806256e-18i -2.602085e-18+0.000000e+00i
[2,] 2.515349e-17-3.469447e-18i 3.851860e-34+1.637040e-33i 1.734723e-18+6.505213e-18i -1.040834e-17-7.806256e-18i
[3,] -1.734723e-18+8.673617e-19i 1.213336e-32-9.629650e-35i -2.602085e-18+6.938894e-18i -1.040834e-17-2.645453e-17i
[4,] 1.387779e-17-6.722053e-18i 0.000000e+00-2.311116e-33i -6.765422e-17+1.734723e-18i 8.673617e-18+1.734723e-18i
[5,] -8.673617e-19+9.540979e-18i -3.851860e-34-4.188898e-33i 6.938894e-18+5.421011e-18i 0.000000e+00-7.372575e-18i
[6,] 5.000000e-01-0.000000e+00i -9.629650e-34-2.888895e-33i -8.673617e-19-8.023096e-18i 1.214306e-17-1.691355e-17i
[7,] -1.040834e-17-6.071532e-18i 1.224606e-16+0.000000e+00i 6.938894e-18+5.421011e-18i -1.040834e-17-8.239937e-18i
[8,] -8.673617e-19-2.406929e-17i -7.896313e-33+9.629650e-34i -5.000000e-01-0.000000e+00i -1.214306e-17+5.811324e-17i
[9,] -8.673617e-19+1.387779e-17i 9.629650e-34-5.488900e-33i -8.673617e-19+2.775558e-17i -8.660254e-01-0.000000e+00i
[10,] -8.673617e-19+2.385245e-18i -3.274081e-33-1.829633e-33i -2.255141e-17-4.987330e-18i -3.469447e-18+2.753874e-17i
[,10] [,11] [,12] [,13]
[1,] -8.673617e-18+1.821460e-17i -1.734723e-18-8.673617e-19i -8.673617e-19+1.734723e-18i 0.000000e+00-3.851860e-34i
[2,] 5.724587e-17+5.204170e-18i 7.806256e-18-1.040834e-17i 0.000000e+00+1.257675e-17i -3.851860e-34+2.311116e-33i
[3,] 1.734723e-18-6.071532e-18i 5.030698e-17-2.775558e-17i 1.734723e-18+4.336809e-18i -3.466674e-33-3.274081e-33i
[4,] -3.122502e-17+2.862294e-17i 6.938894e-18-6.071532e-18i 5.551115e-17+3.903128e-18i -7.703720e-34-4.237046e-33i
[5,] -2.255141e-17+2.255141e-17i 1.387779e-17-2.211772e-17i 8.673617e-19-3.469447e-18i 2.465190e-32+9.629650e-34i
[6,] -8.673617e-18+1.734723e-17i 2.255141e-17-3.035766e-18i 2.602085e-18+1.474515e-17i -1.540744e-33-1.155558e-33i
[7,] -6.938894e-18+3.035766e-18i -1.144917e-16+7.372575e-18i -2.602085e-18+2.168404e-18i -5.007418e-33+1.925930e-34i
[8,] -2.949030e-17-6.808790e-17i -8.673617e-18-2.558717e-17i -4.336809e-17+2.537033e-17i 3.466674e-33+1.540744e-33i
[9,] 1.734723e-18+7.719519e-17i 3.469447e-18-1.257675e-17i -2.602085e-18-2.081668e-17i 1.540744e-33+2.503709e-33i
[10,] -1.000000e+00-0.000000e+00i 2.081668e-17-9.887924e-17i 1.734723e-17-9.540979e-18i 5.007418e-33+3.851860e-33i
[,14] [,15] [,16] [,17]
[1,] 4.770490e-18-1.734723e-18i 6.938894e-18-1.734723e-18i 1.734723e-18-8.673617e-18i 1.214306e-17+3.469447e-18i
[2,] 1.647987e-17-1.604619e-17i 2.602085e-18+6.071532e-18i -1.734723e-18+3.469447e-18i 7.806256e-18-6.071532e-18i
[3,] 5.204170e-18+2.602085e-18i -1.561251e-17+2.428613e-17i 2.602085e-18-6.938894e-18i 0.000000e+00+9.540979e-18i
[4,] 0.000000e+00-4.770490e-18i -1.734723e-18-1.214306e-17i 8.673617e-19-2.602085e-17i 8.673617e-19+1.734723e-18i
[5,] 3.469447e-18-9.540979e-18i 1.734723e-18-1.734723e-18i 6.938894e-18+1.214306e-17i -4.423545e-17-3.469447e-18i
[6,] -8.239937e-17+0.000000e+00i 1.734723e-18-2.602085e-18i -1.734723e-18-2.602085e-18i 2.602085e-18+9.540979e-18i
[7,] -2.602085e-18-1.387779e-17i -1.422473e-16+9.540979e-18i 0.000000e+00+6.071532e-18i 1.561251e-17-1.040834e-17i
[8,] 1.734723e-18-1.387779e-17i 6.938894e-18-1.647987e-17i -1.994932e-16+1.734723e-18i 1.734723e-18+1.647987e-17i
[9,] -5.204170e-18-1.301043e-18i 3.469447e-18+2.732189e-17i -3.469447e-18+1.561251e-17i 5.204170e-17+0.000000e+00i
[10,] 2.688821e-17-2.818926e-18i 0.000000e+00+5.637851e-18i -2.602085e-17-7.979728e-17i 1.734723e-18-2.602085e-17i
[,18] [,19] [,20] [,21]
[1,] 1.301043e-18+3.469447e-18i 2.118523e-33+0.000000e+00i 1.734723e-18+4.336809e-18i 1.734723e-18+1.561251e-17i
[2,] 8.239937e-18-1.734723e-18i -5.777790e-34-1.925930e-33i 4.336809e-19+8.673617e-19i -4.336809e-18-3.469447e-18i
[3,] 0.000000e+00-8.673617e-19i 1.117039e-32+7.703720e-34i 2.168404e-18+8.673617e-19i -8.673617e-19+0.000000e+00i
[4,] -2.168404e-18+8.673617e-19i 1.925930e-33+0.000000e+00i -1.257675e-17-1.734723e-18i 5.204170e-18+1.040834e-17i
[5,] -1.301043e-18+0.000000e+00i 2.311116e-33+7.703720e-34i 4.336809e-18+1.734723e-18i -1.301043e-17-2.862294e-17i
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[2,] 7.806256e-18-3.469447e-18i -1.734723e-18-1.734723e-18i -1.734723e-18+1.734723e-18i 8.673617e-19+0.000000e+00i
[3,] 1.734723e-18-4.336809e-19i -1.387779e-17-2.775558e-17i -4.336809e-18+1.734723e-18i -7.806256e-18+8.673617e-19i
[4,] 0.000000e+00+4.336809e-19i -1.734723e-18+0.000000e+00i 2.602085e-18-6.938894e-18i 0.000000e+00+0.000000e+00i
[5,] -8.673617e-19+0.000000e+00i 8.673617e-19+0.000000e+00i 1.734723e-18+0.000000e+00i -1.734723e-18+6.938894e-18i
[6,] 2.081668e-17-1.040834e-17i 0.000000e+00+0.000000e+00i 0.000000e+00+8.673617e-19i -8.673617e-19+0.000000e+00i
[7,] 8.673617e-19+4.336809e-19i 1.214306e-17-2.081668e-17i 1.734723e-18-8.673617e-19i 7.806256e-18-8.673617e-19i
[8,] 0.000000e+00+0.000000e+00i -3.469447e-18-8.673617e-19i 1.561251e-17+6.938894e-18i -1.734723e-18+0.000000e+00i
[9,] 0.000000e+00-6.505213e-19i 0.000000e+00+4.336809e-19i 1.734723e-18-8.673617e-19i -1.734723e-18+6.071532e-18i
[10,] 6.938894e-18+6.938894e-18i 0.000000e+00-8.673617e-19i 1.734723e-18+0.000000e+00i 3.469447e-18+8.673617e-19i
[,66] [,67] [,68] [,69]
[1,] -4.336809e-19-8.673617e-19i 6.162976e-33+1.848893e-32i 6.505213e-19+0.000000e+00i 4.336809e-19-1.214306e-17i
[2,] 4.336809e-19-6.071532e-18i -9.244464e-33+1.232595e-32i 4.770490e-18-8.673617e-19i 8.673617e-19+0.000000e+00i
[3,] 1.301043e-18-1.734723e-18i -9.860761e-32+9.860761e-32i 1.301043e-18+0.000000e+00i -4.336809e-19-1.734723e-18i
[4,] -3.469447e-18+3.469447e-18i 1.232595e-32-3.081488e-32i -1.951564e-17+6.071532e-18i 3.469447e-18-3.469447e-18i
[5,] -1.734723e-18+0.000000e+00i 2.465190e-32-6.162976e-33i 3.903128e-18-2.602085e-18i 2.775558e-17-1.387779e-17i
[6,] -5.637851e-18+6.938894e-18i 6.162976e-33-1.232595e-32i 3.035766e-18+0.000000e+00i 0.000000e+00-8.673617e-19i
[7,] 1.734723e-18-4.336809e-19i -4.930381e-32+4.314083e-32i -4.336809e-19-8.673617e-19i 4.336809e-18+0.000000e+00i
[8,] -8.673617e-19+0.000000e+00i 0.000000e+00-1.232595e-32i 1.301043e-18+6.938894e-18i 0.000000e+00+8.673617e-19i
[9,] 0.000000e+00+0.000000e+00i 6.162976e-33-6.162976e-33i -8.673617e-19+0.000000e+00i 1.561251e-17+0.000000e+00i
[10,] 7.806256e-18+1.734723e-17i -1.232595e-32+0.000000e+00i 3.469447e-18-4.336809e-19i 1.734723e-18-8.673617e-19i
[,70] [,71] [,72] [,73]
[1,] 2.168404e-18+3.469447e-18i -6.938894e-18+1.734723e-18i 3.252607e-19+0.000000e+00i 0.000000e+00+0.000000e+00i
[2,] 8.673617e-19-2.775558e-17i -1.301043e-18+3.469447e-18i -2.168404e-19+0.000000e+00i -6.740755e-33+3.081488e-33i
[3,] 2.602085e-18+3.469447e-18i -1.214306e-17-6.938894e-18i -4.336809e-19-8.673617e-19i -3.851860e-34+3.081488e-33i
[4,] 1.734723e-18-5.204170e-18i -3.903128e-18+0.000000e+00i -5.637851e-18-6.938894e-18i 2.696302e-33+0.000000e+00i
[5,] -1.734723e-18-1.734723e-18i 6.071532e-18-1.734723e-18i -4.336809e-19+8.673617e-19i -2.157042e-32+0.000000e+00i
[6,] 1.474515e-17-2.775558e-17i 0.000000e+00+0.000000e+00i 4.336809e-19-8.673617e-19i -6.933348e-33+3.081488e-33i
[7,] 6.938894e-18-5.204170e-18i -4.163336e-17+1.387779e-17i -4.336809e-19-8.673617e-19i 8.474092e-33+0.000000e+00i
[8,] -1.734723e-18+0.000000e+00i 0.000000e+00-8.673617e-19i 1.387779e-17-1.301043e-17i 3.081488e-33+0.000000e+00i
[9,] 3.469447e-18-3.469447e-18i 0.000000e+00+0.000000e+00i -1.734723e-18+8.673617e-19i -2.465190e-32+1.232595e-32i
[10,] 0.000000e+00+1.040834e-17i -1.734723e-18+8.673617e-19i 0.000000e+00+0.000000e+00i 1.540744e-33+0.000000e+00i
[,74] [,75] [,76] [,77]
[1,] 1.084202e-18-8.673617e-19i -4.770490e-18+0.000000e+00i -1.734723e-18-1.734723e-18i -1.344411e-17-2.775558e-17i
[2,] -6.830474e-18+0.000000e+00i -1.192622e-18+1.734723e-18i -1.734723e-18-6.938894e-18i -3.035766e-18+1.734723e-18i
[3,] -7.589415e-19-8.673617e-19i 4.141652e-17+1.387779e-17i 8.673617e-19-3.469447e-18i 7.372575e-18-1.734723e-18i
[4,] 2.168404e-19+3.469447e-18i 2.168404e-18-1.734723e-18i 2.862294e-17+1.734723e-18i -2.168404e-19+0.000000e+00i
[5,] 8.673617e-19-8.673617e-19i 4.770490e-18-1.734723e-18i -5.637851e-18+1.734723e-18i 4.293441e-17+1.734723e-18i
[6,] 1.973248e-17+6.071532e-18i 6.505213e-19+0.000000e+00i -6.505213e-18-1.734723e-18i -1.734723e-18+0.000000e+00i
[7,] 2.602085e-18-2.602085e-18i 1.301043e-18-1.734723e-18i -2.602085e-18+0.000000e+00i -2.168404e-18-6.938894e-18i
[8,] -8.673617e-19+0.000000e+00i 4.770490e-18-3.469447e-18i -1.431147e-17-1.734723e-18i -1.301043e-18+1.734723e-18i
[9,] -1.734723e-18+1.734723e-18i 4.336809e-18+0.000000e+00i 0.000000e+00+3.469447e-18i 1.387779e-17-1.387779e-17i
[10,] -6.505213e-18+8.673617e-19i -8.673617e-19-1.734723e-18i 8.673617e-19+1.734723e-18i 1.734723e-18-1.734723e-18i
[,78] [,79] [,80] [,81]
[1,] -1.517883e-18+8.673617e-19i 4.622232e-32+0.000000e+00i -2.602085e-18+1.734723e-18i 8.673617e-19+2.602085e-18i
[2,] 1.387779e-17-8.673617e-19i 5.238529e-32-4.930381e-32i 2.602085e-18+1.734723e-18i -2.602085e-18-3.469447e-18i
[3,] 4.336809e-19+2.602085e-18i 3.081488e-33+1.047706e-31i -8.673617e-19+3.469447e-18i -5.204170e-18-1.734723e-18i
[4,] 1.192622e-18+0.000000e+00i -3.389637e-32+2.465190e-32i -4.336809e-19+2.168404e-17i 6.071532e-18-3.469447e-18i
[5,] 4.336809e-19+0.000000e+00i -1.232595e-32+1.232595e-32i -2.168404e-19+3.469447e-18i -1.387779e-17+1.387779e-17i
[6,] -6.288373e-18+1.474515e-17i 1.232595e-32-2.465190e-32i -1.084202e-18+8.673617e-19i 3.903128e-18-3.469447e-18i
[7,] -2.602085e-18+1.734723e-18i 1.910523e-31-3.451266e-31i -2.818926e-18+1.734723e-18i 0.000000e+00+0.000000e+00i
[8,] 4.336809e-19+8.673617e-19i 1.540744e-32+0.000000e+00i -4.336809e-19+4.857226e-17i -1.734723e-18+1.734723e-18i
[9,] 1.951564e-18-1.734723e-18i -4.622232e-32+6.162976e-33i -8.673617e-19+8.673617e-19i 4.076600e-17+1.127570e-16i
[10,] 1.387779e-17+6.071532e-18i -3.081488e-33-1.232595e-32i -4.336809e-19+2.602085e-18i -8.673617e-19+0.000000e+00i
[,82] [,83] [,84] [,85]
[1,] 3.469447e-18+5.204170e-18i 8.673617e-19+8.673617e-19i -8.673617e-19+0.000000e+00i 1.540744e-33+0.000000e+00i
[2,] 1.908196e-17+2.255141e-17i -1.734723e-18+1.734723e-18i -2.168404e-18-8.673617e-19i 3.081488e-33+1.078521e-32i
[3,] -2.602085e-18+3.469447e-18i -1.734723e-18+2.255141e-17i -1.734723e-18+8.673617e-19i -3.081488e-33+5.238529e-32i
[4,] 1.734723e-18-3.469447e-18i 7.806256e-18+1.734723e-18i 1.734723e-18-1.127570e-17i 4.622232e-33+2.157042e-32i
[5,] 8.673617e-19-1.734723e-18i 5.204170e-18+0.000000e+00i 1.734723e-18+8.673617e-19i 1.032298e-31-6.162976e-33i
[6,] -1.301043e-17+2.775558e-17i -2.602085e-18-1.734723e-18i 0.000000e+00-6.938894e-18i 0.000000e+00-3.081488e-33i
[7,] -4.336809e-19+3.469447e-18i -1.387779e-17+1.734723e-18i 2.168404e-19-2.602085e-18i -9.244464e-33+0.000000e+00i
[8,] 5.637851e-18+0.000000e+00i -2.602085e-18+0.000000e+00i -7.155734e-18+6.938894e-18i -2.311116e-33-3.081488e-33i
[9,] 2.602085e-18-1.734723e-18i 0.000000e+00-1.734723e-18i 1.734723e-18+0.000000e+00i -3.851860e-33+0.000000e+00i
[10,] 2.949030e-17+6.765422e-17i 8.673617e-19-3.469447e-18i 4.336809e-19-8.673617e-19i 1.540744e-33-9.244464e-33i
[,86] [,87] [,88] [,89]
[1,] -1.734723e-18-2.602085e-18i 2.602085e-18+8.673617e-19i -1.734723e-18-1.561251e-17i 5.030698e-17+5.290907e-17i
[2,] 1.431147e-17+1.474515e-17i -8.673617e-19+5.204170e-18i 0.000000e+00+1.040834e-17i 4.336809e-18+8.673617e-19i
[3,] -8.673617e-19-1.734723e-18i -1.387779e-17-2.515349e-17i 1.734723e-18+3.469447e-18i 3.469447e-18-1.214306e-17i
[4,] -1.344411e-17-1.734723e-18i 5.204170e-18-6.071532e-18i 2.168404e-17+2.688821e-17i 2.602085e-18+8.673617e-18i
[5,] 3.035766e-18+0.000000e+00i -1.734723e-18-1.734723e-18i -5.204170e-18-1.734723e-18i 5.464379e-17+2.775558e-17i
[6,] -2.818926e-17+2.602085e-17i 6.938894e-18-6.071532e-18i -8.673617e-19-1.040834e-17i -2.602085e-18-1.734723e-18i
[7,] -1.301043e-18-6.071532e-18i -5.377643e-17+2.862294e-17i -8.673617e-19-1.734723e-18i 8.673617e-19-1.127570e-17i
[8,] -2.602085e-18+2.602085e-18i 8.673617e-19-3.469447e-18i -7.112366e-17+5.724587e-17i 5.204170e-18+1.040834e-17i
[9,] 1.084202e-18-1.734723e-18i 8.673617e-19+0.000000e+00i -8.673617e-19+3.469447e-18i 1.474515e-17-2.602085e-17i
[10,] -2.168404e-19+6.071532e-18i -4.336809e-19-3.469447e-18i 2.602085e-18-3.469447e-18i 6.071532e-18-1.734723e-18i
[,90] [,91] [,92] [,93]
[1,] -6.071532e-18+5.204170e-18i -4.314083e-32-3.081488e-32i 8.673617e-18-2.385245e-18i -1.214306e-17+3.035766e-18i
[2,] -1.214306e-17+1.301043e-18i -8.628166e-32-3.081488e-32i 1.734723e-18-2.168404e-18i 2.081668e-17+1.734723e-18i
[3,] 1.734723e-18-7.806256e-18i -2.095412e-31+1.848893e-32i 0.000000e+00+8.673617e-19i 1.040834e-17-3.079134e-17i
[4,] -6.071532e-18-6.938894e-18i 1.232595e-32-1.848893e-32i 0.000000e+00-8.673617e-19i 1.734723e-18-8.673617e-19i
[5,] 4.336809e-18-4.336809e-19i -4.930381e-32+1.047706e-31i -1.734723e-18-4.336809e-18i -5.637851e-17+2.775558e-17i
[6,] 4.119968e-17+2.775558e-17i 1.232595e-32+1.232595e-32i 6.938894e-18-9.107298e-18i -1.734723e-18+3.469447e-18i
[7,] 2.602085e-18-2.602085e-18i 5.916457e-31+1.232595e-32i -8.673617e-19-1.734723e-18i 6.938894e-18+0.000000e+00i
[8,] -2.602085e-18-6.938894e-18i 1.848893e-32-6.779273e-32i 3.989864e-17+2.515349e-17i -1.734723e-18-8.673617e-19i
[9,] 3.035766e-18-8.673617e-19i -5.546678e-32+9.860761e-32i 4.336809e-18+0.000000e+00i 6.852158e-17+1.734723e-18i
[10,] 4.336809e-19-8.673617e-19i 0.000000e+00+6.162976e-33i 2.602085e-18+5.204170e-18i 1.734723e-18+7.806256e-18i
[,94] [,95] [,96]
[1,] -1.040834e-17+2.168404e-18i 3.122502e-17+7.372575e-18i -1.561251e-17+5.009014e-17i
[2,] -5.724587e-17-1.205633e-16i 8.673617e-18+4.163336e-17i -1.734723e-18-2.688821e-17i
[3,] -2.081668e-17+2.602085e-18i 5.551115e-17-5.637851e-17i -1.734723e-18+1.214306e-17i
[4,] -6.938894e-18+5.030698e-17i 0.000000e+00+1.040834e-17i 2.862294e-17-2.797242e-17i
[5,] -6.938894e-18+3.469447e-18i 1.734723e-17+2.341877e-17i 8.673617e-19+5.637851e-18i
[6,] -1.092876e-16+4.336809e-18i -1.734723e-18-1.040834e-17i 8.673617e-19-1.734723e-18i
[7,] 3.469447e-18-1.561251e-17i -2.428613e-17+5.030698e-17i 3.469447e-18-3.903128e-18i
[8,] -3.469447e-18+2.775558e-17i 1.127570e-17+8.673617e-18i -2.949030e-17+2.255141e-17i
[9,] 0.000000e+00-1.734723e-18i -1.387779e-17-8.673617e-19i 2.602085e-18+4.770490e-18i
[10,] 2.775558e-17-3.209238e-17i -8.673617e-19-1.040834e-17i -8.673617e-19-1.301043e-17i
[ достигнута getOption("max.print") -- пропущено 86 строк ]plot(1:L, res_comp_wise[[1]][, 2])Предупреждение в xy.coords(x, y, xlabel, ylabel, log) :
мнимые части убраны при преобразовании
avr <- averaging(res_comp_wise)
for (i in 1:dim(res$t_series)[2]){
plot(x, avr[i, ])
}Ошибка в 1:dim(res$t_series)[2] :аргумент нулевой длиныn <- 96*2-1
x <- 0:(n-1)
L <- 96
y <- sin(2*pi/12 * x)
X <- hankel(y, L)
Ft <- dftmtx(L) / sqrt(L)
Ft_inv <- t(Conj(Ft))
component_wise_mult <- function(index){
Ft %*% t(sweep(Ft_inv, 1, X[, index], '*'))
}
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, nrow = n, ncol = L)
for (i in 1:K){
res[i:(i+L-1), ] <- res[i:(i+L-1), ] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[i, ] <- res[i, ] / counters[i]
}
res
}
res_comp_wise <- lapply(1:L, component_wise_mult)
print(res_comp_wise[[1]]) [,1] [,2] [,3] [,4] [,5]
[1,] 0+0i 1.387779e-17-4.374756e-17i 2.255141e-17+1.778092e-17i -1.561251e-17+1.994932e-17i -5.377643e-17-6.505213e-18i
[2,] 0+0i 5.000000e-01+0.000000e+00i 6.938894e-18-6.776264e-17i 1.561251e-17-6.418477e-17i -6.938894e-18+1.170938e-17i
[3,] 0+0i 1.040834e-17-2.569559e-17i 8.660254e-01+0.000000e+00i -3.989864e-17-3.165870e-17i -5.898060e-17-3.361027e-17i
[4,] 0+0i -2.949030e-17+2.634611e-17i 6.938894e-17-2.667137e-17i 1.000000e+00-0.000000e+00i 2.949030e-17-1.994932e-17i
[5,] 0+0i 5.204170e-18-4.987330e-18i -1.734723e-17-2.602085e-18i 2.949030e-17+0.000000e+00i 8.660254e-01-0.000000e+00i
[6,] 0+0i 5.204170e-18+6.505213e-18i 0.000000e+00-3.187554e-17i -5.377643e-17-1.431147e-17i -3.469447e-18+1.144917e-16i
[7,] 0+0i 3.469447e-18-4.770490e-18i -2.775558e-17-4.336809e-19i -3.469447e-18-6.071532e-18i 2.255141e-17-2.168404e-18i
[8,] 0+0i -1.734723e-18+1.647987e-17i 0.000000e+00-8.673617e-18i -1.144917e-16+1.149254e-16i -6.938894e-18-1.214306e-17i
[9,] 0+0i 0.000000e+00+6.071532e-18i 1.734723e-18-5.637851e-18i 0.000000e+00+1.734723e-18i 5.204170e-17-1.301043e-17i
[10,] 0+0i -8.673617e-19-4.336809e-19i -5.204170e-18-5.204170e-18i 2.949030e-17+5.204170e-18i 1.040834e-17+3.469447e-18i
[,6] [,7] [,8] [,9]
[1,] 0.000000e+00+4.987330e-18i 5.777790e-34-3.274081e-33i -3.469447e-18+7.806256e-18i -2.602085e-18+0.000000e+00i
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[,90] [,91] [,92] [,93]
[1,] -6.071532e-18+5.204170e-18i -4.314083e-32-3.081488e-32i 8.673617e-18-2.385245e-18i -1.214306e-17+3.035766e-18i
[2,] -1.214306e-17+1.301043e-18i -8.628166e-32-3.081488e-32i 1.734723e-18-2.168404e-18i 2.081668e-17+1.734723e-18i
[3,] 1.734723e-18-7.806256e-18i -2.095412e-31+1.848893e-32i 0.000000e+00+8.673617e-19i 1.040834e-17-3.079134e-17i
[4,] -6.071532e-18-6.938894e-18i 1.232595e-32-1.848893e-32i 0.000000e+00-8.673617e-19i 1.734723e-18-8.673617e-19i
[5,] 4.336809e-18-4.336809e-19i -4.930381e-32+1.047706e-31i -1.734723e-18-4.336809e-18i -5.637851e-17+2.775558e-17i
[6,] 4.119968e-17+2.775558e-17i 1.232595e-32+1.232595e-32i 6.938894e-18-9.107298e-18i -1.734723e-18+3.469447e-18i
[7,] 2.602085e-18-2.602085e-18i 5.916457e-31+1.232595e-32i -8.673617e-19-1.734723e-18i 6.938894e-18+0.000000e+00i
[8,] -2.602085e-18-6.938894e-18i 1.848893e-32-6.779273e-32i 3.989864e-17+2.515349e-17i -1.734723e-18-8.673617e-19i
[9,] 3.035766e-18-8.673617e-19i -5.546678e-32+9.860761e-32i 4.336809e-18+0.000000e+00i 6.852158e-17+1.734723e-18i
[10,] 4.336809e-19-8.673617e-19i 0.000000e+00+6.162976e-33i 2.602085e-18+5.204170e-18i 1.734723e-18+7.806256e-18i
[,94] [,95] [,96]
[1,] -1.040834e-17+2.168404e-18i 3.122502e-17+7.372575e-18i -1.561251e-17+5.009014e-17i
[2,] -5.724587e-17-1.205633e-16i 8.673617e-18+4.163336e-17i -1.734723e-18-2.688821e-17i
[3,] -2.081668e-17+2.602085e-18i 5.551115e-17-5.637851e-17i -1.734723e-18+1.214306e-17i
[4,] -6.938894e-18+5.030698e-17i 0.000000e+00+1.040834e-17i 2.862294e-17-2.797242e-17i
[5,] -6.938894e-18+3.469447e-18i 1.734723e-17+2.341877e-17i 8.673617e-19+5.637851e-18i
[6,] -1.092876e-16+4.336809e-18i -1.734723e-18-1.040834e-17i 8.673617e-19-1.734723e-18i
[7,] 3.469447e-18-1.561251e-17i -2.428613e-17+5.030698e-17i 3.469447e-18-3.903128e-18i
[8,] -3.469447e-18+2.775558e-17i 1.127570e-17+8.673617e-18i -2.949030e-17+2.255141e-17i
[9,] 0.000000e+00-1.734723e-18i -1.387779e-17-8.673617e-19i 2.602085e-18+4.770490e-18i
[10,] 2.775558e-17-3.209238e-17i -8.673617e-19-1.040834e-17i -8.673617e-19-1.301043e-17i
[ достигнута getOption("max.print") -- пропущено 86 строк ]plot(1:L, res_comp_wise[[1]][, 2])Предупреждение в xy.coords(x, y, xlabel, ylabel, log) :
мнимые части убраны при преобразовании
avr <- averaging(res_comp_wise)
for (i in 1:dim(res$t_series)[2]){
plot(x, avr[i, ])
}Ошибка в 1:dim(res$t_series)[2] :аргумент нулевой длиныCiSSA через Фурье
n <- 96*2-1
x <- 0:(n-1)
L <- 96
y <- sin(2*pi/12 * x)
X <- hankel(y, L)
Ft <- dftmtx(L) / sqrt(L)
Ft_inv <- t(Conj(Ft))
component_wise_mult <- function(index){
Ft %*% t(sweep(Ft_inv, 1, X[, index], '*'))
}
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, nrow = n, ncol = L)
for (i in 1:K){
res[i:(i+L-1), ] <- res[i:(i+L-1), ] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[i, ] <- res[i, ] / counters[i]
}
res
}
res_comp_wise <- lapply(1:L, component_wise_mult)
print(res_comp_wise[[1]]) [,1] [,2] [,3] [,4] [,5]
[1,] 0+0i 1.387779e-17-4.374756e-17i 2.255141e-17+1.778092e-17i -1.561251e-17+1.994932e-17i -5.377643e-17-6.505213e-18i
[2,] 0+0i 5.000000e-01+0.000000e+00i 6.938894e-18-6.776264e-17i 1.561251e-17-6.418477e-17i -6.938894e-18+1.170938e-17i
[3,] 0+0i 1.040834e-17-2.569559e-17i 8.660254e-01+0.000000e+00i -3.989864e-17-3.165870e-17i -5.898060e-17-3.361027e-17i
[4,] 0+0i -2.949030e-17+2.634611e-17i 6.938894e-17-2.667137e-17i 1.000000e+00-0.000000e+00i 2.949030e-17-1.994932e-17i
[5,] 0+0i 5.204170e-18-4.987330e-18i -1.734723e-17-2.602085e-18i 2.949030e-17+0.000000e+00i 8.660254e-01-0.000000e+00i
[6,] 0+0i 5.204170e-18+6.505213e-18i 0.000000e+00-3.187554e-17i -5.377643e-17-1.431147e-17i -3.469447e-18+1.144917e-16i
[7,] 0+0i 3.469447e-18-4.770490e-18i -2.775558e-17-4.336809e-19i -3.469447e-18-6.071532e-18i 2.255141e-17-2.168404e-18i
[8,] 0+0i -1.734723e-18+1.647987e-17i 0.000000e+00-8.673617e-18i -1.144917e-16+1.149254e-16i -6.938894e-18-1.214306e-17i
[9,] 0+0i 0.000000e+00+6.071532e-18i 1.734723e-18-5.637851e-18i 0.000000e+00+1.734723e-18i 5.204170e-17-1.301043e-17i
[10,] 0+0i -8.673617e-19-4.336809e-19i -5.204170e-18-5.204170e-18i 2.949030e-17+5.204170e-18i 1.040834e-17+3.469447e-18i
[,6] [,7] [,8] [,9]
[1,] 0.000000e+00+4.987330e-18i 5.777790e-34-3.274081e-33i -3.469447e-18+7.806256e-18i -2.602085e-18+0.000000e+00i
[2,] 2.515349e-17-3.469447e-18i 3.851860e-34+1.637040e-33i 1.734723e-18+6.505213e-18i -1.040834e-17-7.806256e-18i
[3,] -1.734723e-18+8.673617e-19i 1.213336e-32-9.629650e-35i -2.602085e-18+6.938894e-18i -1.040834e-17-2.645453e-17i
[4,] 1.387779e-17-6.722053e-18i 0.000000e+00-2.311116e-33i -6.765422e-17+1.734723e-18i 8.673617e-18+1.734723e-18i
[5,] -8.673617e-19+9.540979e-18i -3.851860e-34-4.188898e-33i 6.938894e-18+5.421011e-18i 0.000000e+00-7.372575e-18i
[6,] 5.000000e-01-0.000000e+00i -9.629650e-34-2.888895e-33i -8.673617e-19-8.023096e-18i 1.214306e-17-1.691355e-17i
[7,] -1.040834e-17-6.071532e-18i 1.224606e-16+0.000000e+00i 6.938894e-18+5.421011e-18i -1.040834e-17-8.239937e-18i
[8,] -8.673617e-19-2.406929e-17i -7.896313e-33+9.629650e-34i -5.000000e-01-0.000000e+00i -1.214306e-17+5.811324e-17i
[9,] -8.673617e-19+1.387779e-17i 9.629650e-34-5.488900e-33i -8.673617e-19+2.775558e-17i -8.660254e-01-0.000000e+00i
[10,] -8.673617e-19+2.385245e-18i -3.274081e-33-1.829633e-33i -2.255141e-17-4.987330e-18i -3.469447e-18+2.753874e-17i
[,10] [,11] [,12] [,13]
[1,] -8.673617e-18+1.821460e-17i -1.734723e-18-8.673617e-19i -8.673617e-19+1.734723e-18i 0.000000e+00-3.851860e-34i
[2,] 5.724587e-17+5.204170e-18i 7.806256e-18-1.040834e-17i 0.000000e+00+1.257675e-17i -3.851860e-34+2.311116e-33i
[3,] 1.734723e-18-6.071532e-18i 5.030698e-17-2.775558e-17i 1.734723e-18+4.336809e-18i -3.466674e-33-3.274081e-33i
[4,] -3.122502e-17+2.862294e-17i 6.938894e-18-6.071532e-18i 5.551115e-17+3.903128e-18i -7.703720e-34-4.237046e-33i
[5,] -2.255141e-17+2.255141e-17i 1.387779e-17-2.211772e-17i 8.673617e-19-3.469447e-18i 2.465190e-32+9.629650e-34i
[6,] -8.673617e-18+1.734723e-17i 2.255141e-17-3.035766e-18i 2.602085e-18+1.474515e-17i -1.540744e-33-1.155558e-33i
[7,] -6.938894e-18+3.035766e-18i -1.144917e-16+7.372575e-18i -2.602085e-18+2.168404e-18i -5.007418e-33+1.925930e-34i
[8,] -2.949030e-17-6.808790e-17i -8.673617e-18-2.558717e-17i -4.336809e-17+2.537033e-17i 3.466674e-33+1.540744e-33i
[9,] 1.734723e-18+7.719519e-17i 3.469447e-18-1.257675e-17i -2.602085e-18-2.081668e-17i 1.540744e-33+2.503709e-33i
[10,] -1.000000e+00-0.000000e+00i 2.081668e-17-9.887924e-17i 1.734723e-17-9.540979e-18i 5.007418e-33+3.851860e-33i
[,14] [,15] [,16] [,17]
[1,] 4.770490e-18-1.734723e-18i 6.938894e-18-1.734723e-18i 1.734723e-18-8.673617e-18i 1.214306e-17+3.469447e-18i
[2,] 1.647987e-17-1.604619e-17i 2.602085e-18+6.071532e-18i -1.734723e-18+3.469447e-18i 7.806256e-18-6.071532e-18i
[3,] 5.204170e-18+2.602085e-18i -1.561251e-17+2.428613e-17i 2.602085e-18-6.938894e-18i 0.000000e+00+9.540979e-18i
[4,] 0.000000e+00-4.770490e-18i -1.734723e-18-1.214306e-17i 8.673617e-19-2.602085e-17i 8.673617e-19+1.734723e-18i
[5,] 3.469447e-18-9.540979e-18i 1.734723e-18-1.734723e-18i 6.938894e-18+1.214306e-17i -4.423545e-17-3.469447e-18i
[6,] -8.239937e-17+0.000000e+00i 1.734723e-18-2.602085e-18i -1.734723e-18-2.602085e-18i 2.602085e-18+9.540979e-18i
[7,] -2.602085e-18-1.387779e-17i -1.422473e-16+9.540979e-18i 0.000000e+00+6.071532e-18i 1.561251e-17-1.040834e-17i
[8,] 1.734723e-18-1.387779e-17i 6.938894e-18-1.647987e-17i -1.994932e-16+1.734723e-18i 1.734723e-18+1.647987e-17i
[9,] -5.204170e-18-1.301043e-18i 3.469447e-18+2.732189e-17i -3.469447e-18+1.561251e-17i 5.204170e-17+0.000000e+00i
[10,] 2.688821e-17-2.818926e-18i 0.000000e+00+5.637851e-18i -2.602085e-17-7.979728e-17i 1.734723e-18-2.602085e-17i
[,18] [,19] [,20] [,21]
[1,] 1.301043e-18+3.469447e-18i 2.118523e-33+0.000000e+00i 1.734723e-18+4.336809e-18i 1.734723e-18+1.561251e-17i
[2,] 8.239937e-18-1.734723e-18i -5.777790e-34-1.925930e-33i 4.336809e-19+8.673617e-19i -4.336809e-18-3.469447e-18i
[3,] 0.000000e+00-8.673617e-19i 1.117039e-32+7.703720e-34i 2.168404e-18+8.673617e-19i -8.673617e-19+0.000000e+00i
[4,] -2.168404e-18+8.673617e-19i 1.925930e-33+0.000000e+00i -1.257675e-17-1.734723e-18i 5.204170e-18+1.040834e-17i
[5,] -1.301043e-18+0.000000e+00i 2.311116e-33+7.703720e-34i 4.336809e-18+1.734723e-18i -1.301043e-17-2.862294e-17i
[6,] -1.257675e-17-1.647987e-17i -3.851860e-34+4.622232e-33i 4.336809e-19+0.000000e+00i 1.734723e-18-2.602085e-18i
[7,] 0.000000e+00+1.734723e-18i -2.465190e-32-3.851860e-34i 4.336809e-19-8.673617e-19i 1.734723e-18-2.602085e-18i
[8,] 6.938894e-18+1.734723e-18i -1.540744e-33+3.851860e-34i -4.293441e-17+5.377643e-17i -8.673617e-19-6.071532e-18i
[9,] -8.673617e-19+3.469447e-18i 1.540744e-33-3.851860e-34i 2.602085e-18-3.035766e-18i -5.377643e-17+5.204170e-17i
[10,] -1.387779e-17+1.301043e-17i -7.703720e-34-6.933348e-33i 8.673617e-19+1.561251e-17i -2.602085e-18-5.204170e-18i
[,22] [,23] [,24] [,25]
[1,] 4.336809e-19+1.734723e-18i 6.071532e-18-5.204170e-18i -1.355253e-18-8.673617e-19i 0.000000e+00+0.000000e+00i
[2,] 1.214306e-17+1.387779e-17i -2.602085e-18+0.000000e+00i -2.602085e-18-8.673617e-19i -4.814825e-35+0.000000e+00i
[3,] 4.336809e-18-1.734723e-18i -4.163336e-17+0.000000e+00i 8.673617e-19-8.673617e-19i -3.274081e-33+0.000000e+00i
[4,] -1.734723e-18-1.387779e-17i 1.734723e-18-1.734723e-18i -1.994932e-17+0.000000e+00i 1.925930e-34+2.311116e-33i
[5,] 6.938894e-18+6.938894e-18i -4.336809e-19+6.938894e-18i 2.168404e-18+1.734723e-18i 0.000000e+00-2.311116e-33i
[6,] -5.464379e-17-5.204170e-17i 0.000000e+00+6.938894e-18i 2.602085e-18-2.602085e-18i -2.503709e-33+0.000000e+00i
[7,] 3.469447e-18-6.938894e-18i -4.336809e-17-5.724587e-17i 1.734723e-18-8.673617e-19i 3.851860e-34-2.311116e-33i
[8,] -1.734723e-18+2.255141e-17i -2.602085e-18-1.214306e-17i -4.119968e-17-1.127570e-17i -3.851860e-34-3.081488e-33i
[9,] -3.469447e-18+0.000000e+00i 1.734723e-18-8.673617e-19i 8.673617e-19-2.602085e-18i 0.000000e+00-7.703720e-34i
[10,] -8.847090e-17+5.464379e-17i -1.734723e-18-1.387779e-17i -4.336809e-19+1.734723e-18i -1.155558e-33+0.000000e+00i
[,26] [,27] [,28] [,29]
[1,] -2.710505e-19+0.000000e+00i 2.385245e-18+5.204170e-18i -1.734723e-18-3.469447e-18i 1.604619e-17+1.387779e-17i
[2,] 1.382358e-17-1.301043e-17i 6.071532e-18+6.938894e-18i 0.000000e+00-6.938894e-18i -4.336809e-19+1.734723e-18i
[3,] 5.421011e-20-8.673617e-19i 1.431147e-17+1.734723e-18i -8.673617e-19-3.469447e-18i -6.505213e-19+0.000000e+00i
[4,] 3.252607e-18-8.673617e-19i -1.517883e-18+0.000000e+00i -8.673617e-19+1.734723e-18i 8.673617e-19-1.734723e-18i
[5,] -8.673617e-19+2.602085e-18i 1.084202e-18+0.000000e+00i 2.168404e-18-1.734723e-18i -2.775558e-17-2.949030e-17i
[6,] 6.938894e-18+0.000000e+00i -4.336809e-19+1.734723e-18i -5.637851e-18+0.000000e+00i -1.301043e-18-1.734723e-18i
[7,] 4.553649e-18+3.469447e-18i 2.862294e-17-3.989864e-17i 2.602085e-18-1.734723e-18i 1.734723e-18+0.000000e+00i
[8,] 8.673617e-19+0.000000e+00i 2.602085e-18+1.734723e-18i 5.421011e-17+1.387779e-17i 3.469447e-18+3.469447e-18i
[9,] 4.336809e-19+1.734723e-18i -1.301043e-18+1.734723e-18i -3.469447e-18-1.734723e-18i 4.336809e-19+1.214306e-17i
[10,] 4.336809e-19-2.602085e-18i -1.734723e-18-3.469447e-18i 8.673617e-19+5.204170e-18i 6.505213e-18+5.204170e-18i
[,30] [,31] [,32] [,33]
[1,] 6.505213e-19+8.673617e-19i 0.000000e+00+0.000000e+00i 1.301043e-18-8.673617e-19i -2.688821e-17+0.000000e+00i
[2,] 7.155734e-18+8.673617e-19i 4.622232e-33-3.081488e-33i -4.336809e-19-8.673617e-19i -3.469447e-18+1.734723e-18i
[3,] 8.673617e-19+8.673617e-19i -2.619265e-32+0.000000e+00i 1.301043e-18+2.602085e-18i -6.938894e-18-1.734723e-18i
[4,] 1.084202e-18+0.000000e+00i 4.622232e-33+0.000000e+00i -6.505213e-19+7.806256e-18i 1.301043e-18+3.469447e-18i
[5,] -1.084202e-18+0.000000e+00i -2.696302e-32-1.540744e-32i 8.673617e-19+3.469447e-18i -1.474515e-17+0.000000e+00i
[6,] -5.854692e-18-2.168404e-17i -1.540744e-33+6.162976e-33i -2.168404e-19+0.000000e+00i -1.301043e-18+1.734723e-18i
[7,] -1.517883e-18-1.734723e-18i 2.187856e-31-4.930381e-32i -6.505213e-19-8.673617e-19i 5.637851e-18-1.734723e-18i
[8,] -3.035766e-18+3.469447e-18i -6.162976e-33+0.000000e+00i -6.505213e-18+2.081668e-17i -3.469447e-18-3.469447e-18i
[9,] 1.517883e-18+2.602085e-18i -2.465190e-32+3.081488e-33i 0.000000e+00+8.673617e-19i -6.722053e-17-2.775558e-17i
[10,] -6.505213e-19-6.071532e-18i -1.386670e-32-1.848893e-32i 2.168404e-19-3.469447e-18i -1.734723e-18-3.469447e-18i
[,34] [,35] [,36] [,37]
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[8,] -8.673617e-19+0.000000e+00i 4.770490e-18-3.469447e-18i -1.431147e-17-1.734723e-18i -1.301043e-18+1.734723e-18i
[9,] -1.734723e-18+1.734723e-18i 4.336809e-18+0.000000e+00i 0.000000e+00+3.469447e-18i 1.387779e-17-1.387779e-17i
[10,] -6.505213e-18+8.673617e-19i -8.673617e-19-1.734723e-18i 8.673617e-19+1.734723e-18i 1.734723e-18-1.734723e-18i
[,78] [,79] [,80] [,81]
[1,] -1.517883e-18+8.673617e-19i 4.622232e-32+0.000000e+00i -2.602085e-18+1.734723e-18i 8.673617e-19+2.602085e-18i
[2,] 1.387779e-17-8.673617e-19i 5.238529e-32-4.930381e-32i 2.602085e-18+1.734723e-18i -2.602085e-18-3.469447e-18i
[3,] 4.336809e-19+2.602085e-18i 3.081488e-33+1.047706e-31i -8.673617e-19+3.469447e-18i -5.204170e-18-1.734723e-18i
[4,] 1.192622e-18+0.000000e+00i -3.389637e-32+2.465190e-32i -4.336809e-19+2.168404e-17i 6.071532e-18-3.469447e-18i
[5,] 4.336809e-19+0.000000e+00i -1.232595e-32+1.232595e-32i -2.168404e-19+3.469447e-18i -1.387779e-17+1.387779e-17i
[6,] -6.288373e-18+1.474515e-17i 1.232595e-32-2.465190e-32i -1.084202e-18+8.673617e-19i 3.903128e-18-3.469447e-18i
[7,] -2.602085e-18+1.734723e-18i 1.910523e-31-3.451266e-31i -2.818926e-18+1.734723e-18i 0.000000e+00+0.000000e+00i
[8,] 4.336809e-19+8.673617e-19i 1.540744e-32+0.000000e+00i -4.336809e-19+4.857226e-17i -1.734723e-18+1.734723e-18i
[9,] 1.951564e-18-1.734723e-18i -4.622232e-32+6.162976e-33i -8.673617e-19+8.673617e-19i 4.076600e-17+1.127570e-16i
[10,] 1.387779e-17+6.071532e-18i -3.081488e-33-1.232595e-32i -4.336809e-19+2.602085e-18i -8.673617e-19+0.000000e+00i
[,82] [,83] [,84] [,85]
[1,] 3.469447e-18+5.204170e-18i 8.673617e-19+8.673617e-19i -8.673617e-19+0.000000e+00i 1.540744e-33+0.000000e+00i
[2,] 1.908196e-17+2.255141e-17i -1.734723e-18+1.734723e-18i -2.168404e-18-8.673617e-19i 3.081488e-33+1.078521e-32i
[3,] -2.602085e-18+3.469447e-18i -1.734723e-18+2.255141e-17i -1.734723e-18+8.673617e-19i -3.081488e-33+5.238529e-32i
[4,] 1.734723e-18-3.469447e-18i 7.806256e-18+1.734723e-18i 1.734723e-18-1.127570e-17i 4.622232e-33+2.157042e-32i
[5,] 8.673617e-19-1.734723e-18i 5.204170e-18+0.000000e+00i 1.734723e-18+8.673617e-19i 1.032298e-31-6.162976e-33i
[6,] -1.301043e-17+2.775558e-17i -2.602085e-18-1.734723e-18i 0.000000e+00-6.938894e-18i 0.000000e+00-3.081488e-33i
[7,] -4.336809e-19+3.469447e-18i -1.387779e-17+1.734723e-18i 2.168404e-19-2.602085e-18i -9.244464e-33+0.000000e+00i
[8,] 5.637851e-18+0.000000e+00i -2.602085e-18+0.000000e+00i -7.155734e-18+6.938894e-18i -2.311116e-33-3.081488e-33i
[9,] 2.602085e-18-1.734723e-18i 0.000000e+00-1.734723e-18i 1.734723e-18+0.000000e+00i -3.851860e-33+0.000000e+00i
[10,] 2.949030e-17+6.765422e-17i 8.673617e-19-3.469447e-18i 4.336809e-19-8.673617e-19i 1.540744e-33-9.244464e-33i
[,86] [,87] [,88] [,89]
[1,] -1.734723e-18-2.602085e-18i 2.602085e-18+8.673617e-19i -1.734723e-18-1.561251e-17i 5.030698e-17+5.290907e-17i
[2,] 1.431147e-17+1.474515e-17i -8.673617e-19+5.204170e-18i 0.000000e+00+1.040834e-17i 4.336809e-18+8.673617e-19i
[3,] -8.673617e-19-1.734723e-18i -1.387779e-17-2.515349e-17i 1.734723e-18+3.469447e-18i 3.469447e-18-1.214306e-17i
[4,] -1.344411e-17-1.734723e-18i 5.204170e-18-6.071532e-18i 2.168404e-17+2.688821e-17i 2.602085e-18+8.673617e-18i
[5,] 3.035766e-18+0.000000e+00i -1.734723e-18-1.734723e-18i -5.204170e-18-1.734723e-18i 5.464379e-17+2.775558e-17i
[6,] -2.818926e-17+2.602085e-17i 6.938894e-18-6.071532e-18i -8.673617e-19-1.040834e-17i -2.602085e-18-1.734723e-18i
[7,] -1.301043e-18-6.071532e-18i -5.377643e-17+2.862294e-17i -8.673617e-19-1.734723e-18i 8.673617e-19-1.127570e-17i
[8,] -2.602085e-18+2.602085e-18i 8.673617e-19-3.469447e-18i -7.112366e-17+5.724587e-17i 5.204170e-18+1.040834e-17i
[9,] 1.084202e-18-1.734723e-18i 8.673617e-19+0.000000e+00i -8.673617e-19+3.469447e-18i 1.474515e-17-2.602085e-17i
[10,] -2.168404e-19+6.071532e-18i -4.336809e-19-3.469447e-18i 2.602085e-18-3.469447e-18i 6.071532e-18-1.734723e-18i
[,90] [,91] [,92] [,93]
[1,] -6.071532e-18+5.204170e-18i -4.314083e-32-3.081488e-32i 8.673617e-18-2.385245e-18i -1.214306e-17+3.035766e-18i
[2,] -1.214306e-17+1.301043e-18i -8.628166e-32-3.081488e-32i 1.734723e-18-2.168404e-18i 2.081668e-17+1.734723e-18i
[3,] 1.734723e-18-7.806256e-18i -2.095412e-31+1.848893e-32i 0.000000e+00+8.673617e-19i 1.040834e-17-3.079134e-17i
[4,] -6.071532e-18-6.938894e-18i 1.232595e-32-1.848893e-32i 0.000000e+00-8.673617e-19i 1.734723e-18-8.673617e-19i
[5,] 4.336809e-18-4.336809e-19i -4.930381e-32+1.047706e-31i -1.734723e-18-4.336809e-18i -5.637851e-17+2.775558e-17i
[6,] 4.119968e-17+2.775558e-17i 1.232595e-32+1.232595e-32i 6.938894e-18-9.107298e-18i -1.734723e-18+3.469447e-18i
[7,] 2.602085e-18-2.602085e-18i 5.916457e-31+1.232595e-32i -8.673617e-19-1.734723e-18i 6.938894e-18+0.000000e+00i
[8,] -2.602085e-18-6.938894e-18i 1.848893e-32-6.779273e-32i 3.989864e-17+2.515349e-17i -1.734723e-18-8.673617e-19i
[9,] 3.035766e-18-8.673617e-19i -5.546678e-32+9.860761e-32i 4.336809e-18+0.000000e+00i 6.852158e-17+1.734723e-18i
[10,] 4.336809e-19-8.673617e-19i 0.000000e+00+6.162976e-33i 2.602085e-18+5.204170e-18i 1.734723e-18+7.806256e-18i
[,94] [,95] [,96]
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[2,] -5.724587e-17-1.205633e-16i 8.673617e-18+4.163336e-17i -1.734723e-18-2.688821e-17i
[3,] -2.081668e-17+2.602085e-18i 5.551115e-17-5.637851e-17i -1.734723e-18+1.214306e-17i
[4,] -6.938894e-18+5.030698e-17i 0.000000e+00+1.040834e-17i 2.862294e-17-2.797242e-17i
[5,] -6.938894e-18+3.469447e-18i 1.734723e-17+2.341877e-17i 8.673617e-19+5.637851e-18i
[6,] -1.092876e-16+4.336809e-18i -1.734723e-18-1.040834e-17i 8.673617e-19-1.734723e-18i
[7,] 3.469447e-18-1.561251e-17i -2.428613e-17+5.030698e-17i 3.469447e-18-3.903128e-18i
[8,] -3.469447e-18+2.775558e-17i 1.127570e-17+8.673617e-18i -2.949030e-17+2.255141e-17i
[9,] 0.000000e+00-1.734723e-18i -1.387779e-17-8.673617e-19i 2.602085e-18+4.770490e-18i
[10,] 2.775558e-17-3.209238e-17i -8.673617e-19-1.040834e-17i -8.673617e-19-1.301043e-17i
[ достигнута getOption("max.print") -- пропущено 86 строк ]plot(1:L, res_comp_wise[[1]][, 2])Предупреждение в xy.coords(x, y, xlabel, ylabel, log) :
мнимые части убраны при преобразовании
avr <- averaging(res_comp_wise)
for (i in 1:dim(res$t_series)[2]){
plot(x, avr[i, ])
}Ошибка в 1:dim(res$t_series)[2] :аргумент нулевой длины# Ft %*% sweep(Ft_inv, 1, X[, 1], '*')[2, ]reconstruct_fft <- function(x, y, frequencies) {
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
reconstructed <- matrix(0, length(amplitudes), length(x))
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
# print(i)
reconstructed[i, ] <-
amplitudes[i] *
cos(2 * pi * frequencies[i] * (x) + phases[i]) /
n
}
# plot(x, reconstructed[9, ], main = paste(x[1]), type = "l", col = "red")
# lines(x, y/2)
# plot(x, reconstructed[L+2-9, ], main = paste(x[1]))
return(reconstructed)
}
n <- 96*2-1
x <- 0:(n-1)
L <- 48
frequencies <- (0:(L-1)) / L
y <- sin(2*pi/12 * x)
y_main <- y
x_main <- x
X <- hankel(y, L)
K <- dim(X)[2]
res <- list()
for (i in 1:K){
y <- X[, i]
x <- x_main[1:(1 + L - 1)]
res[[i]] <- reconstruct_fft(x, y, frequencies)
}
# for (i in 1:L){
# plot(x, res[[i]][9, ])
# }
res_mult <- res
# res
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, ncol = n, nrow = L)
for (i in 1:length(res_comp_wise_mult)){
res[, i:(i+L-1)] <- res[, i:(i+L-1)] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[, i] <- res[, i] / counters[i]
}
res
}
avr <- averaging(res_mult)
group_by_elementary_freq_foureir <- function(res_averaged){
nf2 <- 0
if (L %% 2) {
nf2 <- (L + 1) / 2 - 1
} else {
nf2 <- L / 2 - 1
}
nft <- nf2 + abs((L %% 2) - 2)
Z <- matrix(0, ncol = nft, nrow = n)
# print(Z |> dim())
# print(res_averaged |> dim())
Z[, 1] <- res_averaged[1, ]
for (k in 1:nf2) {
Z[, k + 1] <- res_averaged[k + 1, ] + res_averaged[L + 2 - (k + 1), ]
}
if (L %% 2 != 0) {
Z[, nft] <- res_averaged[nft, ]
}
return(list(
t_series = Z,
freq = (0:dim(Z)[2])/L
))
}
rs <- group_by_elementary_freq_foureir(avr)
plot(x_main, rs$t_series[, 5])
IP_values
data_slice <- 1:537
dates_slice <- dates[data_slice]
IP_values_slice <- IP_values[data_slice]
eps <- 1/193
c <- circulant_SSA(IP_values_slice, L = 192, extend_flag = FALSE)
r <- c$t_series
reconstruct_fft <- function(x, y, frequencies) {
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
reconstructed <- matrix(0, length(amplitudes), length(x))
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
# print(i)
reconstructed[i, ] <-
amplitudes[i] *
cos(2 * pi * frequencies[i] * (x) + phases[i]) /
n
}
# plot(x, reconstructed[9, ], main = paste(x[1]), type = "l", col = "red")
# lines(x, y/2)
# plot(x, reconstructed[L+2-9, ], main = paste(x[1]))
return(reconstructed)
}
n <- 537
x <- 0:(n-1)
L <- 192
frequencies <- (0:(L-1)) / L
y <- IP_values_slice
y_main <- y
x_main <- x
X <- hankel(y, L)
K <- dim(X)[2]
res <- list()
for (i in 1:K){
y <- X[, i]
x <- x_main[1:(1 + L - 1)]
res[[i]] <- reconstruct_fft(x, y, frequencies)
}
# for (i in 1:L){
# plot(x, res[[i]][9, ])
# }
res_mult <- res
# res
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, ncol = n, nrow = L)
for (i in 1:length(res_comp_wise_mult)){
res[, i:(i+L-1)] <- res[, i:(i+L-1)] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[, i] <- res[, i] / counters[i]
}
res
}
avr <- averaging(res_mult)
group_by_elementary_freq_foureir <- function(res_averaged){
nf2 <- 0
if (L %% 2) {
nf2 <- (L + 1) / 2 - 1
} else {
nf2 <- L / 2 - 1
}
nft <- nf2 + abs((L %% 2) - 2)
Z <- matrix(0, ncol = nft, nrow = n)
# print(Z |> dim())
# print(res_averaged |> dim())
Z[, 1] <- res_averaged[1, ]
for (k in 1:nf2) {
Z[, k + 1] <- res_averaged[k + 1, ] + res_averaged[L + 2 - (k + 1), ]
}
if (L %% 2 != 0) {
Z[, nft] <- res_averaged[nft, ]
}
return(list(
t_series = Z,
freq = (0:dim(Z)[2])/L
))
}
rs <- group_by_elementary_freq_foureir(avr)
# plot(x_main, rs$t_series[, 5])
for (i in 1:dim(r)[2]){
plot(1:n, rs$t_series[, i], col= "red", type = "l")
lines(1:n, r[, i])
}
cissa_like_fourier_transform <- function(ts, L){
reconstruct_fft <- function(x, y, frequencies) {
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
reconstructed <- matrix(0, length(amplitudes), length(x))
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
# print(i)
reconstructed[i, ] <-
amplitudes[i] *
cos(2 * pi * frequencies[i] * (x) + phases[i]) /
n
}
# plot(x, reconstructed[9, ], main = paste(x[1]), type = "l", col = "red")
# lines(x, y/2)
# plot(x, reconstructed[L+2-9, ], main = paste(x[1]))
return(reconstructed)
}
n <- length(ts)
x <- 0:(n-1)
L <- L
frequencies <- (0:(L-1)) / L
y <- ts
y_main <- y
x_main <- x
X <- hankel(y, L)
K <- dim(X)[2]
res <- list()
for (i in 1:K){
y <- X[, i]
x <- x_main[1:(1 + L - 1)]
res[[i]] <- reconstruct_fft(x, y, frequencies)
}
# for (i in 1:L){
# plot(x, res[[i]][9, ])
# }
res_mult <- res
# res
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, ncol = n, nrow = L)
for (i in 1:length(res_comp_wise_mult)){
res[, i:(i+L-1)] <- res[, i:(i+L-1)] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[, i] <- res[, i] / counters[i]
}
res
}
avr <- averaging(res_mult)
group_by_elementary_freq_foureir <- function(res_averaged){
nf2 <- 0
if (L %% 2) {
nf2 <- (L + 1) / 2 - 1
} else {
nf2 <- L / 2 - 1
}
nft <- nf2 + abs((L %% 2) - 2)
Z <- matrix(0, ncol = nft, nrow = n)
# print(Z |> dim())
# print(res_averaged |> dim())
Z[, 1] <- res_averaged[1, ]
for (k in 1:nf2) {
Z[, k + 1] <- res_averaged[k + 1, ] + res_averaged[L + 2 - (k + 1), ]
}
if (L %% 2 != 0) {
Z[, nft] <- res_averaged[nft, ]
}
return(list(
t_series = Z,
freq = (0:dim(Z)[2])/L
))
}
rs <- group_by_elementary_freq_foureir(avr)
return(rs)
}
data_slice <- 1:537
dates_slice <- dates[data_slice]
IP_values_slice <- IP_values[data_slice]
eps <- 1/193
c <- circulant_SSA(IP_values_slice, L = 192, extend_flag = FALSE)
r <- c$t_series
c_ft <- cissa_like_fourier_transform(IP_values_slice, L = 192)
r_ft <- c_ft$t_series
for (i in 1:dim(r)[2]){
plot(1:n, r_ft[, i], col= "red", type = "l", lwd = 2)
lines(1:n, r[, i])
}
---
title: "Circulant SSA"
author: "Погребников Николай"
output: html_notebook
---

## Вспомогательные функции

```{r}
library(Rssa)
library(signal)
library(gsignal)
source("eossa_new.R")


dftmtx <- function(n) {
  y <- stats::mvfft(diag(1, n))
  y
}

diag_averaging <- function(A){
  B <- A[nrow(A):1, ] |> Re()
  lapply(split(B, -(row(B) - col(B)) ), mean) |> as.numeric()
}

shift_vector <- function(vec) {
  last_element <- tail(vec, 1)
  vec <- vec[-length(vec)]
  shifted_vec <- c(last_element, vec)
  return(shifted_vec)
}

extend <- function(x, H){
  # Вычисление коэффициентов AR модели для дифференцированного ряда
  N <- length(x)
  p <- floor(N / 3)
  dx <- diff(x)
  # A <- ar(dx, order.max = p, method = "yule-walker")$ar
  A <- aryule(dx, p)$a
  
  # Правое расширение
  y <- x
  dy <- diff(y)
  er <- signal::filter(A, 1, dy)
  dy <- signal::filter(1, A, c(er, rep(0, H)))
  y <- y[1] + c(0, cumsum(dy))
  
  # Левое расширение
  y <- rev(y)
  dy <- diff(y)
  er <- signal::filter(A,1,dy)
  dy <- signal::filter(1,A,c(er, rep(0, H)))
  y <- y[1] + c(0, cumsum(dy))
  
  # Расширенный ряд
  xe <- rev(y)
  
  # Вывод результатов
  xe 
}
```

## CiSSA

Подаётся на вход временной ряд, длина окна (если её нет, то она равна длине ряда + 1 пополам) и информация о том, нужно ли расширить ряд. Расширять ряд стоит при стохастическом тренде (Autoregressive extension (default). It is indicated for stationary and stochastic trend time series as well). Реализовано только Autoregressive extension.

\
На выходе список выдаётся список list(t_series, importance).\
t_series — матрица, по столбцам которой располагаются временные ряды, отвечающие за частоты (i-1)/L, где i — номер столбца, L — длина окна.\
importance — вектор, отвечающий за значимость i-ого временного ряда в разлолжении. Чем больше значение, тем больший вклад внёс i-тый временной ряд.

```{r}
circulant_SSA <- function(ts, L = NULL, extend_flag = FALSE){
  time_series <- ts
  # Construct trajectory matrix
  N <- length(time_series)
  if (is.null(L)){
    L <- (N + 1)%/%2
  }
  # Проверка на расширения ряда
  if (extend_flag == FALSE){
    H <- 0
    time_series <- ts
  }
  else{
    H <- L
    time_series <- extend(ts, H)
  }
  
  X <- hankel(time_series, L)
  
  # Number of symmetric frequency pairs around 1/2
  if (L %% 2) {
    nf2 <- (L + 1) / 2 - 1
  } else {
    nf2 <- L / 2 - 1
  }
  
  # Number of frequencies <= 1/2
  nft <- nf2 + abs((L %% 2) - 2)
  
  # Decomposition
  # Estimate autocovariance     OK
  autocov <- numeric(L)
  for (m in 0:(L-1)){
    autocov[[m+1]] <- sum(time_series[1:(N-m)] * time_series[(1+m):N]) / (N-m)
  }
  
  # First row of circulant matrix
  circ_first_row <- numeric(L)
  for (m in 0:(L-1)){
    circ_first_row[[m+1]] <- (L-m)/L * autocov[[m+1]] + (m)/L * autocov[[L-m]]
  }
  
  # Build circulant matrix
  S_C <- matrix(circ_first_row, nrow = 1)
  shifted_vector <- circ_first_row
  for (i in 2:(L)) {
    shifted_vector <- shift_vector(shifted_vector)
    # S_C <- rbind(S_C, as.vector(shifted_vector))
    S_C <- rbind(as.vector(shifted_vector), S_C)
  }
  
  # Eigenvectors of circulant matrix (unitary base)
  U <- dftmtx(L)/sqrt(L)
  
  # Real eigenvectors (orthonormal base)
  U[, 1] <- Re(U[, 1])
  for (k in 1:nf2) {
    u_k <- U[, k + 1]
    U[, k + 1] <- sqrt(2) * Re(u_k)
    U[, L + 2 - (k + 1)] <- sqrt(2) * Im(u_k)
  }
  if (L %% 2 != 0) {
    U[, nft] <- Re(U[, nft])
  }
  
  # Eigenvalues of circulant matrix: estimated power spectral density
  psd <- abs(diag(t(U) %*% S_C %*% U))
  
  # Principal components
  W <- t(U) %*% X
  # Reconstruction
  # Elementary reconstructed series
  R <- matrix(0, nrow = N+2*H, ncol = L)
  for (k in 1:L) {
    R[, k] <- U[ ,k] %*% t(W[k, ]) |> diag_averaging()
  }
  
  # Grouping by frequency
  # Elementary reconstructed series by frequency
  Z <- matrix(0, nrow = N+2*H, ncol = nft)
  Z[, 1] <- R[, 1]
  # Importance of component
  imp <- numeric(nft)
  lambda_sm <- sum(psd)
  imp[1] <- psd[1]/lambda_sm
  for (k in 1:nf2) {
    Z[, k + 1] <- R[, k + 1] + R[, L + 2 - (k + 1)]
    imp[k+1] <- (psd[k+1] + psd[ L + 2 - (k + 1)])/lambda_sm
  }
  if (L %% 2 != 0) {
    Z[, nft] <- R[, nft]
    imp[nft] <- psd[nft] / lambda_sm
  }
  
  list(t_series = Z[(H+1):(N+H),],
       importance = imp,
       freq = (0:(length(imp) -1))/L
       )
}
```

```{r}
# groups - list of frequencies
grouping_cissa <- function(cissa_res, groups){
  freq <- cissa_res$freq
  t_series <- cissa_res$t_series
  
  residuals <- 0
  result <- setNames(as.list(rep(0, length(groups))), names(groups))
  for (i in 1:length(cissa_res$freq)){
    flag <- FALSE
    for (name in names(groups)){
      if (groups[[name]][1] <= freq[i] & freq[i] <= groups[[name]][2]){
        flag <- TRUE
        result[[name]] <- result[[name]] + t_series[, i]
      }
    }
    
    if (flag == FALSE){
      residuals <- residuals + t_series[, i]
    }
  }
  
  result[["residuals"]] <- residuals
  result
}
```

```{r}
generate_ts <- function(func, n=1e3, ...){
  1:n |> func(...) |> ts()
}

f_cos <- function(x, A = 1, omega = 1/4, phi = 0){
  f_exp_mod_harm_series(x, A, alpha = 0, omega = omega, phi = phi)
}

f_sin <- function(x, A = 1, omega = 1/4, phi = 3*pi/2){
  f_exp_mod_harm_series(x, A, alpha = 0, omega = omega, phi = phi)
}

f_exp <- function(x, A = 1, alpha = 1){
  A * exp(alpha * x)
}

f_exp_cos <- function(x, A = 1, alpha = 1, omega = 1/4, phi = 0){
  f_exp_mod_harm_series(x, A, alpha, omega, phi)
}

f_const <- function(x, C = 0){
  rep(C, length(x))
}

f_exp_mod_harm_series <- function(x, A = 1, alpha = 1, omega = 1/4, phi = 0){
  A*exp(alpha*x)*cos(2*pi*omega*x + phi)
}

f_linear <- function(x, a = 1, b = 0){
  a*x + b
}
mse <- function(f_true, f_reconstructed){
   mean((f_true - f_reconstructed)^2) 
}
```

#### Ошибка при Lw in N, Kw not in N

```{r}
n <- 96*2+5
L <- 96
f_sum <- function(x){
  f_const(x, C = 1) + f_cos(x, omega = 1/12) 
}


f_const |> generate_ts(n, C = 1) |>
  plot(col = "green", ylim = c(-1, 2), ylab = "f_n")
f_cos |>
  generate_ts(n, omega = 1/12) |>
  lines(col="green")
f_sum |> generate_ts(n) |> lines(lwd = 3, col='red')
f_n <- f_sum(1:n)



c <- circulant_SSA(f_n, L = 96, extend_flag = FALSE)
r <- grouping_cissa(c,
               groups = list(
                 trend = c(0, 1/100),
                 sesonal = c(1/99, 1/10)
               )
               )

f_C <- f_const |> generate_ts(n, C = 1)
f_c <- f_cos |> generate_ts(n, omega = 1/12)
print("Ошибки при CiSSA")
print(paste("Ошибка при вычислении C = 1: ", mse(f_C, r$trend) |> format(scientific = TRUE, digits = 2) ))
print(paste("Ошибка при вычислении cos(pi/12): ", mse(f_c, r$sesonal) |> format(scientific = TRUE, digits = 2) ))

lines(1:n, r$trend, col="blue")
lines(1:n, r$sesonal, col="blue")

f_const |> generate_ts(n, C = 1) |>
  plot(col = "green", ylim = c(-1, 2), ylab = "f_n")
f_cos |>
  generate_ts(n, omega = 1/12) |>
  lines(col="green")
f_sum |> generate_ts(n) |> lines(lwd = 3, col='red')
f_n <- f_sum(1:n)

s <- ssa(f_n, L = 96)
r <- reconstruct(s, groups=list(
  trend = 1,
  sesonal = 2:3
))


print("Ошибки при SSA")
print(paste("Ошибка при вычислении C = 1: ", mse(f_C, r$trend) |> format(scientific = TRUE, digits = 2)  ))
print(paste("Ошибка при вычислении cos(pi/12): ", mse(f_c, r$sesonal) |> format(scientific = TRUE, digits = 2)))

lines(1:n, r$trend)
lines(1:n, r$sesonal)
```

#### Проверка разделимости непериодических компонент + автогруппировка SSA

```{r}
n <- 96*2-1
L <- 96

C <- 1
omega_cs <- 1/12
omega_sn <- 1/24
a <- 1/100
f_sum <- function(x){
  f_const(x, C = C) +
    f_cos(x, omega = omega_cs) +
    f_exp(x, a = a) +
    f_sin(x, omega = omega_sn)
}


f_C <- f_const |> generate_ts(n, C = C)
f_c <- f_cos |> generate_ts(n, omega = omega_cs)
f_s <- f_sin |> generate_ts(n, omega = omega_sn)
f_e <- f_exp |> generate_ts(n, a = a)

f_n <- f_sum(1:n)

library(xtable)

# Шаг 2: Создание примера данных
data <- data.frame(
  Метод = c("SSA", "CiSSA"),
  e_err = c(20, 20),
  c_err = c(23, 35),
  ec_err = c(20, 20),
  sin_err = c (20, 20),
  cos_err = c(1, 1)
)


# Отрисовка ряда f_n
plot(f_n, type = "l", lwd = 3, col = 'red', ylim = c(-2, 10),
     xlab = "Время", ylab = "Значения ряда", main = "Разложение временного ряда")

# Добавление отдельных компонентов (f_C, f_c, f_e)
lines(f_C, col = "blue")  # Компонент f_C
lines(f_c, col = "blue")  # Компонент f_c
lines(f_e, col = "blue")  # Компонент f_e
lines(f_s, col = "blue")

# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"), 
       col = c("red", "blue"), lty = 1, lwd = 3)








c <- circulant_SSA(f_n, L = L, extend_flag = TRUE)
# r <- c$t_series
r <- grouping_cissa(c,
                    groups = list(
                      # trend = c(0, 1/100),
                      trend = c(0, 1/1000),
                      sesonal_cos = c(1/14, 1/10),
                      sesonal_sin = c(1/26, 1/23)
                    ))

data$cos_err[2] <- mse(f_s, r$sesonal_sin) |> formatC(format = "e", digits = 1)
data$sin_err[2] <- mse(f_c, r$sesonal_cos) |> formatC(format = "e", digits = 1)
data$ec_err[2] <- mse(f_C+f_e, r$trend) |> formatC(format = "e", digits = 1)


# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/CiSSA.png")  # сохранение в формате PNG

plot(1:n, f_n, type = "l", lwd=3, ylim= c(-2, 10), col="red",
     xlab = "Время", ylab = "Значения ряда", main = "CiSSA разложение временного ряда")
lines(1:n, r$trend, col = "blue")
lines(1:n, r$sesonal_sin, col = "blue")
lines(1:n, r$sesonal_cos, col = "blue")

# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"), 
       col = c("red", "blue"), lty = 1, lwd = 3)

# dev.off()  # завершение сохранения










s <- ssa(f_n, L)
e <- eossa(s, 1:10, k = 7)

g_sesonal <- grouping.auto(e, base = "eigen",
                   freq.bins = list(trend = c(0.001),
                                    sesonal2 = c(1/25, 1/23),
                                    sesonal1 = c(1/13, 1/11)
                                    ),
                   threshold = 0.1)


r <- Rssa::reconstruct(e, groups=c(list(exp = 1,
                                C = 2
                                ),
                             g_sesonal)
                 )

plot(wcor(e, groups = 1:24), scales = list(at = c(10, 20, 30)))

data$c_err[1] <- mse(f_C, r$C) |> formatC(format = "e", digits = 1)
data$e_err[1] <- mse(f_e, r$exp) |> formatC(format = "e", digits = 1)
data$cos_err[1] <- mse(f_c, r$sesonal1) |> formatC(format = "e", digits = 1)
data$sin_err[1] <- mse(f_s, r$sesonal2) |> formatC(format = "e", digits = 1)
data$ec_err[1] <- mse(f_C+f_e, r$C+r$exp) |> formatC(format = "e", digits = 1)


# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/SSA.png")  # сохранение в формате PNG

plot(1:n, f_n, type = "l", lwd=3, ylim= c(-2, 10), col="red",
     xlab = "Время", ylab = "Значения ряда", main = "SSA разложение временного ряда")

lines(1:n, r$trend, type = "l", col="green")
lines(1:n, r$exp, type = "l", ylim= c(-2, 10), col="blue")
lines(1:n, r$C, col = "blue")
lines(1:n, r$sesonal1, col = "blue")
lines(1:n, r$sesonal2, col = "blue")

# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"), 
       col = c("red", "blue"), lty = 1, lwd = 3)







# Шаг 3: Преобразование данных в формат LaTeX
table_latex <- xtable(data, caption = "Example Table")

# Шаг 4: Вывод таблицы в LaTeX файл
print(table_latex, include.rownames = FALSE)





```

#### Пример cos\*exp

```{r}
n <- 96*2-1
L <- 96
eps <- 1/(L+1)

C <- 1
omega_cs <- 1/12
omega_sn <- 1/24
a <- 1/100
omega_exp <- 1/48
f_sum <- function(x){
    f_cos(x, omega = omega_cs) +
    f_exp_mod_harm_series(x, a = a, omega = omega_exp) +
    f_sin(x, omega = omega_sn)
}


f_c <- f_cos |> generate_ts(n, omega = omega_cs)
f_s <- f_sin |> generate_ts(n, omega = omega_sn)
f_e <- f_exp_mod_harm_series |> generate_ts(n, a = a, omega = omega_exp)

f_n <- f_sum(1:n)

library(xtable)

# Шаг 2: Создание примера данных
data <- data.frame(
  Метод = c("SSA", "CiSSA"),
  exp_err = c(20, 20),
  sin_err = c (20, 20),
  cos_err = c(1, 1)
)


# Отрисовка ряда f_n
plot(f_n, type = "l", lwd = 3, col = 'red', ylim = c(-10, 10),
     xlab = "Время", ylab = "Значения ряда", main = "Разложение временного ряда")

# Добавление отдельных компонентов (f_C, f_c, f_e)
lines(f_c, col = "blue")  # Компонент f_c
lines(f_e, col = "blue")  # Компонент f_e
lines(f_s, col = "blue")

# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"), 
       col = c("red", "blue"), lty = 1, lwd = 3)








c <- circulant_SSA(f_n, L = L, extend_flag = TRUE)
# r <- c$t_series
r <- grouping_cissa(c,
                    groups = list(
                      trend = c(0, 1/26-eps),
                      sesonal_cos = c(1/14, 1/10),
                      sesonal_sin = c(1/26, 1/23)
                    ))

data$cos_err[2] <- mse(f_s, r$sesonal_sin) |> formatC(format = "e", digits = 1)
data$sin_err[2] <- mse(f_c, r$sesonal_cos) |> formatC(format = "e", digits = 1)
data$exp_err[2] <- mse(f_e, r$trend) |> formatC(format = "e", digits = 1)


# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/CiSSA.png")  # сохранение в формате PNG

plot(1:n, f_n, type = "l", lwd=3, ylim= c(-10, 10), col="red",
     xlab = "Время", ylab = "Значения ряда", main = "CiSSA разложение временного ряда")
lines(1:n, r$trend, col = "blue")
lines(1:n, r$sesonal_sin, col = "blue")
lines(1:n, r$sesonal_cos, col = "blue")

# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"), 
       col = c("red", "blue"), lty = 1, lwd = 3)

# dev.off()  # завершение сохранения










s <- ssa(f_n, L)
e <- eossa_new(s, nested.groups = list(1:30), clust_type = "distance")

g_sesonal <- grouping.auto(e, base = "eigen",
                   freq.bins = list(trend = c(1/25-eps),
                                    sesonal2 = c(1/25, 1/23),
                                    sesonal1 = c(1/13, 1/11)
                                    ),
                   threshold = 0.1)


r <- reconstruct(e, groups= g_sesonal)

plot(wcor(e, groups = 1:24), scales = list(at = c(10, 20, 30)))

data$exp_err[1] <- mse(f_e, r$trend)  |> formatC(format = "e", digits = 1)
data$cos_err[1] <- mse(f_c, r$sesonal1) |> formatC(format = "e", digits = 1)
data$sin_err[1] <- mse(f_s, r$sesonal2) |> formatC(format = "e", digits = 1)


# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/SSA.png")  # сохранение в формате PNG

plot(1:n, f_n, type = "l", lwd=3, ylim= c(-10, 10), col="red",
     xlab = "Время", ylab = "Значения ряда", main = "SSA разложение временного ряда")

lines(1:n, r$trend, type = "l", col="blue")
lines(1:n, r$sesonal1, col = "blue")
lines(1:n, r$sesonal2, col = "blue")

# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"), 
       col = c("red", "blue"), lty = 1, lwd = 3)







# Шаг 3: Преобразование данных в формат LaTeX
table_latex <- xtable(data, caption = "Example Table")

# Шаг 4: Вывод таблицы в LaTeX файл
print(table_latex, include.rownames = FALSE)


```

## Данные IP

```{r}
library(readxl)
data <- read_excel("Data/International_Financial_Statistics_.xlsx")
data |> head()
```

Отрисовка данных IP

```{r}
dates <- seq(as.Date("1970-01-01"), as.Date("2018-1-30"), by = "month")
IP_values <- data[2, -c(1, 2)] |> as.double() 
plot(dates, IP_values, type="l")
```

#### Cissa

Отрисовка трендовой составляющей чёрным цветом, основной временной ряд — красным

```{r}
data_slice <- 1:537
dates_slice <- dates[data_slice]
IP_values_slice <- IP_values[data_slice]
eps <- 1/193

c <- circulant_SSA(IP_values_slice, L = 192, extend_flag = TRUE)
r <- c$t_series
r <- grouping_cissa(c,
                    groups = list(
                      trend = c(0, 1/192),
                      cycle = c(1/97, 5/95),
                      sesonal = c(1/13, 1/2+0.0001)
                    )
                    )
r_sesonal <-  grouping_cissa(c,
                             groups = list(
                              s1 = c(16/192 - eps, 16/192 + eps),
                              s2 = c(32/192 - eps, 32/192 + eps),
                              s3 = c(48/192 - eps, 48/192 + eps),
                              s4 = c(64/192 - eps, 64/192 + eps),
                              s5 = c(80/192 - eps, 80/192 + eps),
                              s6 = c(96/192 - eps, 96/192 + eps)
                             )
                             )
# cissa_trend <- r[,1] + r[,2]
# cissa_cycle <- r[, 3:11] |> rowSums()
# cissa_sesonal <- r[, c(17, 33, 49, 65, 81, 97)] |> rowSums()
# cissa_residuals <- IP_values_slice - (cissa_trend + cissa_cycle + cissa_sesonal)

cissa_trend <- r$trend
cissa_cycle <- r$cycle
cissa_sesonal <- Reduce("+", r_sesonal |> within(rm(residuals)))
cissa_residuals <- IP_values_slice - (cissa_trend + cissa_cycle + cissa_sesonal)


plot(dates_slice, IP_values_slice,
     type="l", col = "black")
lines(dates_slice, cissa_trend,
      type="l", col = "red")

plot(dates_slice, cissa_cycle,
     type="l", col = "red")

plot(dates_slice, cissa_sesonal,
     type="l", col = "red")

plot(dates_slice, cissa_residuals,
     type="l", col = "red")

plot(dates_slice, IP_values_slice,
     type="l", col = "black")
lines(dates_slice, cissa_trend+cissa_cycle+cissa_sesonal,
      type="l", col = "red")
```

#### SSA fossa

```{r}
s <- ssa(IP_values_slice, L = 192)
e <- fossa(s)
# e <- eossa_new(s, nested.groups = list(1:30), clust_type = "distance")
eps <- 1/193

groups <- grouping.auto(e,
                   freq.bins = list(trend = c(1/192),
                                    cycle = c(1/97, 5/95),
                                    s1 = c(16/192 - eps, 16/192 + eps),
                                    s2 = c(32/192 - eps, 32/192 + eps),
                                    s3 = c(48/192 - eps, 48/192 + eps),
                                    s4 = c(64/192 - eps, 64/192 + eps),
                                    s5 = c(80/192 - eps, 80/192 + eps),
                                    s6 = c(96/192 - eps, 96/192 + eps)
                                    ),
                   threshold = 0)


plot(wcor(e, groups = 1:30), scales = list(at = c(10, 20, 30)),
     main = "W-correlation matrix SSA (fossa)")

r <- reconstruct(e, groups=groups)

ssa_trend_f <- r$trend
ssa_cycle_f <- r$cycle
ssa_sesonal_f <- r$s1 + r$s2 + r$s3 + r$s4 + r$s5 + r$s6
ssa_residuals_f <- IP_values_slice - (ssa_trend_f + ssa_cycle_f + ssa_sesonal_f)

plot(dates_slice, IP_values_slice,
     type="l", col = "black")
lines(dates_slice, ssa_trend_f,
      type="l", col = "magenta")

plot(dates_slice, ssa_cycle_f, 
     type="l", col = "magenta")

plot(dates_slice, ssa_sesonal_f, 
     type="l", col = "magenta")

plot(dates_slice, ssa_residuals_f,
     type="l", col = "magenta")

```

#### SSA eossa

```{r}
library(Rssa)
source("eossa_new.r")
s <- ssa(IP_values_slice, L = 192)
e <- eossa_new(s, nested.groups = list(1:30), clust_type = "distance")




groups <- grouping.auto(e,
                   freq.bins = list(trend = c(1/192),
                                    cycle = c(1/97, 5/95),
                                    s1 = c(16/192 - eps, 16/192 + eps),
                                    s2 = c(32/192 - eps, 32/192 + eps),
                                    s3 = c(48/192 - eps, 48/192 + eps),
                                    s4 = c(64/192 - eps, 64/192 + eps),
                                    s5 = c(80/192 - eps, 80/192 + eps),
                                    s6 = c(96/192 - eps, 96/192 + eps)
                                    ),
                   threshold = 0)
plot(wcor(e, groups = 1:30), scales = list(at = c(10, 20, 30)),
     main = "W-correlation matrix SSA (eossa)")

r <- reconstruct(e, groups=groups)

ssa_trend <- r$trend
ssa_cycle <- r$cycle
ssa_sesonal <- r$s1 + r$s2 + r$s3 + r$s4 + r$s5 + r$s6
ssa_residuals <- IP_values_slice - (ssa_trend + ssa_cycle + ssa_sesonal)

plot(dates_slice, IP_values_slice,
     type="l", col = "black")
lines(dates_slice, ssa_trend,
      type="l", col = "blue")

plot(dates_slice, ssa_cycle, 
     type="l", col = "blue")

plot(dates_slice, ssa_sesonal, 
     type="l", col = "blue")

plot(dates_slice, ssa_residuals,
     type="l", col = "blue")
```

```{r}
plot(dates_slice, IP_values_slice,
     main = "IP USA тренд",xlab = "Время", ylab = "Значение",
     type="l", col = "black")
lines(dates_slice, ssa_trend,
      type="l", col = "blue", lwd=2)
lines(dates_slice, ssa_trend_f,
      type="l", col = "magenta", lwd=2)
lines(dates_slice, cissa_trend,
      type="l", col = "red", lwd=2)
# Легенда
legend("topleft", legend = c("Весь ряд", "CiSSA тренд", "SSA тренд (eossa)", "SSA тренд (fossa)"), 
       col = c("black", "red", "blue", "magenta"), lty = 1, lwd = 3)


plot(dates_slice, ssa_cycle,
     main = "IP USA цикличность", xlab = "Время", ylab = "Значение",
     type="l", col = "blue", ylim=c(-10, 10), lwd=2)
lines(dates_slice, cissa_cycle,
      type="l", col = "red", lwd=2)
lines(dates_slice, ssa_cycle_f,
      type="l", col = "magenta", lwd=2)
# Легенда
legend("topleft", legend = c("CiSSA", "SSA (eossa)", "SSA (fossa)"), 
       col = c("red", "blue", "magenta"), lty = 1, lwd = 3)

```

```{r}
# Настройка графиков для отображения двух графиков один под другим с общей осью X
layout(matrix(c(1, 2), nrow = 2, byrow = TRUE), heights = c(1, 1.2))

# Построение первого графика
par(mar = c(2, 4, 2, 2)) # Уменьшение нижнего отступа
plot(dates_slice, ssa_sesonal, type = "l", col = "blue", lwd = 1,
     main = "SSA (eossa) сезонность", xlab = "", ylab = "Значение")
# Добавление оси X внизу первого графика, но с пустыми метками
axis(1, labels = FALSE)

# Построение второго графика
par(mar = c(5, 4, 2, 2)) # Увеличение нижнего отступа
plot(dates_slice, ssa_sesonal_f, type = "l", col = "magenta", lwd = 1,
     main = "SSA (fossa) сезонность", xlab = "Время", ylab = "Значение")

par(mar = c(3, 4, 2, 2)) # Увеличение нижнего отступа
plot(dates_slice, cissa_sesonal, type = "l", col = "red", lwd = 1,
     main = "CiSSA сезонность", xlab = "Время", ylab = "Значение")

# Восстановление макета по умолчанию
layout(1)


```

```{r}
plot(dates_slice, ssa_residuals, 
     main = "IP USA остаток", xlab = "Время", ylab = "Значение",
     type="l", col = "blue", ylim=c(-2, 2))
lines(dates_slice, cissa_residuals,
      type="l", col = "red")
lines(dates_slice, ssa_residuals_f,
      type="l", col = "magenta")
legend("topleft", legend = c("CiSSA", "SSA (eossa)", "SSA (fossa)"), 
       col = c("red", "blue", "magenta"), lty = 1, lwd = 3)
```

```{r}
ssa_residuals |> density() |> plot()
cissa_residuals |> density() |> plot()
```

### Отделение сигнала от шума

```{r}
set.seed(100)

n_mse_tests <- function(n){
  n <- 96*2-1
  L <- 96
  sigma <- 0.1
  
  
  C <- 1
  omega_cs <- 1/12
  omega_sn <- 1/24
  a <- 1/100
  f_sum <- function(x){
    f_const(x, C = C) +
      f_cos(x, omega = omega_cs) +
      f_exp(x, a = a) +
      f_sin(x, omega = omega_sn)
  }
  
  
  f_C <- f_const |> generate_ts(n, C = C)
  f_c <- f_cos |> generate_ts(n, omega = omega_cs)
  f_s <- f_sin |> generate_ts(n, omega = omega_sn)
  f_e <- f_exp |> generate_ts(n, a = a)
  
  mse_lst <- list()
  for (i in 1:n) {
    f_noise <- rnorm(n, sd = sigma)
    
    f_n <- f_sum(1:n) + f_noise
    
    
    
    c <- circulant_SSA(f_n, L = L, extend_flag = TRUE)
    # r <- c$t_series
    r <- grouping_cissa(c, groups= list(trend = c(0, 1/1000), 
                                        sesonal2 = c(1/25, 1/23),
                                        sesonal1 = c(1/13, 1/10)
                                        ))
    
    # mse_lst$cissa <- c(mse_lst$cissa, mse(f_sum(1:n), r[, 9] + r[, 5] + r[, 1])) 
    mse_lst$cissa <- c(mse_lst$cissa,
                       mse(f_sum(1:n),
                           r$trend + r$sesonal1 + r$sesonal2)) 
    
    
    
    
    s <- ssa(f_n, L)
    # e <- eossa(s, 1:10, k = 6)
    e <- fossa(s)
    
    g_sesonal <- grouping.auto(e, base = "eigen",
                       freq.bins = list(trend = 1/1000, 
                                        sesonal2 = c(1/25, 1/23),
                                        sesonal1 = c(1/13, 1/10)
                                        ),
                       threshold = 0.5)
    
    r <- reconstruct(e, groups=c(list(exp = 1, C = 2), g_sesonal))
    
    mse_lst$ssa <- 
      c(mse_lst$ssa, mse(f_sum(1:n), r$trend + r$sesonal2 + r$sesonal1))
 
  }
  return(mse_lst)
}

res_mse_test <- n_mse_tests(10000)

```

```{r}
# Оценка плотности
density_estimate_cissa <- density(res_mse_test$cissa)

# Построение графика плотности
plot(density_estimate_cissa, main = "Оценка плотности", 
     xlab = "Значение", ylab = "Плотность", 
     col = "blue", lwd = 2)

density_estimate_ssa <- density(res_mse_test$ssa)

# Построение графика плотности
plot(density_estimate_ssa, main = "Оценка плотности", 
     xlab = "Значение", ylab = "Плотность", 
     col = "blue", lwd = 2)

res_mse_test$cissa |> summary()
res_mse_test$cissa |> sd()
res_mse_test$ssa |> summary()
res_mse_test$ssa |> sd()
```

### Как выполняется расширение ряда

```{r}
IP_values_slice |> extend(192) |> plot(type="l", lwd = 3)
c(rep(0, 192),IP_values_slice) |> lines(type="l", col="red")

```

### Фурье преобразование

```{r}
n <- 96*2
L <- 96

x <- 0:(n-1)
y1 <- cos(2 * pi / 12 * x)  # Первая компонента
y2 <- sin(2 * pi / 48 * x)  # Вторая компонента

# Создаем общий временной ряд
y <- y1 + y2

# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)

# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)

# Индексы для частот
n <- length(y)
frequencies <- (0:(n-1)) / n

# Функция для восстановления компонент
reconstruct_fft <- function(frequencies, amplitudes, phases) {
  reconstructed <- list()
  n <- length(amplitudes)
  for (i in 1:(length(amplitudes))) {
    reconstructed[[i]] <-
      amplitudes[i] * cos(2 * pi * frequencies[i] * x + phases[i]) / n * 2
  }
  return(reconstructed)
}

# y_main <- y
# X <- hankel(y)
# K <- dim(X)[2]
# res <- list()
# for (i in 1:K){
#   y <- X[, i]
#   
#   # Выполняем быстрое преобразование Фурье
#   fft_y <- fft(y)
#   
#   # Получаем амплитуды и фазы
#   amplitudes <- Mod(fft_y)
#   phases <- Arg(fft_y)
#   
#   res[[i]] <- reconstruct_fft(frequencies, amplitudes, phases)
# }
# 
# nft <- res[[1]]
# print(nft |> length())
# res_full <- matrix(0, nrow =  |> length(), )
# 
# for (i in 1:K){
#   res_full <- 
# }

# 
# 
y_reconstructed <- reconstruct_fft(frequencies, amplitudes, phases)

# Строим графики
for (i in 1:(n)){
  plot(x, y_reconstructed[[i]], main = paste(frequencies[i]))

}

plot(x, Reduce("+", y_reconstructed), type = "l")
# lines(x, y, col = "red", type = "l", lty = 2)
```

```{r}

```

```{r}
x <- 1:100
y <- sin(2*pi*x)
dftmtx(10)[3, 2]
dftmtx(10)[2, 3]
(as.matrix(dftmtx(10)[3, ])) %*% t(as.matrix(Conj(dftmtx(10)[, 3])))
dim( t(as.matrix(Conj(dftmtx(10)[3, ]))))
dim(as.matrix(dftmtx(10)[3, ]))
```

```{r}

X <- matrix(c(32, 21, 23,
           521,631452, 25251,
           1536, 75, 38), nrow= 3)
f_mat <- dftmtx(3) / sqrt(3)
f_mat_inv <- Conj(f_mat)
X
f_mat %*% f_mat_inv %*% X
```

```{r}
data_slice <- 1:538
n <- 96*2
L <- 96

x <- data_slice
y1 <- cos(2 * pi / 12 * x)  # Первая компонента
y2 <- sin(2 * pi / 48 * x)  # Вторая компонента

# Создаем общий временной ряд
y <- IP_values[data_slice]
y_extended <- y |> extend(L)
x <- 1:length(y_extended)
y <- IP_values[data_slice]

# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)

# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)

# Индексы для частот
n <- length(y)
frequencies <- (0:(n-1)) / n

# Функция для восстановления компонент
reconstruct_fft <- function(frequencies, amplitudes, phases) {
  reconstructed <- list()
  n <- length(amplitudes)
  for (i in 1:(length(amplitudes))) {
    reconstructed[[i]] <-
      amplitudes[i] * cos(2 * pi * frequencies[i] * x + phases[i]) / n * 2
  }
  return(reconstructed)
}

y_reconstructed <- reconstruct_fft(frequencies, amplitudes, phases)

# Строим графики
for (i in 1:(n)){
  plot(x, y_reconstructed[[i]], main = paste(frequencies[i]))
  
}
```

```{r}
set.seed(100)
x <- sin(2*pi/5 * 1:20) + cos(2*pi/2 * 1:20)
L <- 10
X <- hankel(x, L)
X
Ft <- dftmtx(L) / sqrt(L)
Ft_inv <- t(Conj(Ft))
# Ft%*%X[,4:10]
# dftmtx(20) %*% t(Conj(dftmtx(20))) %*% as.matrix(x, nrow = 1) / length(x)
# 
# t(Conj(dftmtx(20))) %*% as.matrix(x, nrow = 1)



# Ft %*%  (Ft_inv %*% X |> diag_averaging())
Ft %*% (Ft_inv %*% X[,5:11] |> apply(1, mean) |> unlist())

dsafads <- function(index_beg){
  Ft %*% (Ft_inv %*% X[, index_beg:(index_beg + dim(X)[1] - 1)] |> unlist())
}

lapply(1:(dim(X)[2] - dim(X)[1]), dsafads)

Ft_inv %*% X 
```

```{r}
Ft_inv_X <- Ft_inv %*% X
f1 <- function(index_beg){
  Ft %*% Ft_inv_X[, index_beg:(index_beg + dim(X)[1] - 1)] |> unlist()
}




```

```{r}
Ft__inv_component_wise <- sweep(Ft_inv, 1, X[, 2], '*')
F_t_compose <- Ft %*% Ft__inv_component_wise
F_t_compose
for (i in 1:L) {
  plot(1:L, F_t_compose[, i])
}

sum(F_t_compose[,3])
x[2]
```

### CiSSA через Фурье

```{r}
# n <- 96*2-1
# x <- 0:(n-1)
# L <- 96
# y <- sin(2*pi/12 * x)
# 
# X <- hankel(y, L)
# 
# Ft <- dftmtx(L) / sqrt(L)
# Ft_inv <- t(Conj(Ft))
# 
# component_wise_mult <- function(index){
#   Ft %*% t(sweep(Ft_inv, 1, X[, index], '*'))
# }
# 
# 
# averaging <- function(res_comp_wise_mult){
#   K <- dim(X)[2]
#   counters <- rep(0, n)
#   res <- matrix(0, nrow = n, ncol = L)
#   for (i in 1:K){
#     res[i:(i+L-1), ] <- res[i:(i+L-1), ] + res_comp_wise_mult[[i]]
#     counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
#   }
#   for (i in 1:n){
#     res[i, ] <- res[i, ] / counters[i]
#   }
#   res
# }
# 
# 
# res_comp_wise <- lapply(1:L, component_wise_mult)
# print(res_comp_wise[[1]])
# 
# 
# plot(1:L, res_comp_wise[[1]][, 2])
# 
# avr <- averaging(res_comp_wise)
# 
# for (i in 1:dim(res$t_series)[2]){
#   plot(x, avr[i, ])
# }
# 
# # plot(x, rowSums(avr))
# 
# group_by_elementary_freq_foureir <- function(res_averaged){
#   nf2 <- 0
#   if (L %% 2) {
#     nf2 <- (L + 1) / 2 - 1
#   } else {
#     nf2 <- L / 2 - 1
#   }
#   nft <- nf2 + abs((L %% 2) - 2)
#   
#   Z <- matrix(0, ncol = nft, nrow = n)
#   
#   # print(Z |> dim())
#   # print(res_averaged |> dim())
#   
#   Z[, 1] <- res_averaged[, 1]
#   for (k in 1:nf2) {
#     Z[, k + 1] <- res_averaged[, k + 1] + res_averaged[, L + 2 - (k + 1)]
#   }
#   if (L %% 2 != 0) {
#     Z[, nft] <- res_averaged[, nft]
#   }
#   
#   
#   return(list(
#     t_series = Z,
#     freq = (0:dim(Z)[2])/L
#   ))
# }
# 
# res <- group_by_elementary_freq_foureir(avr)
# 
# # print(res$t_series |> colSums() |> length())
# # print(x |> length())
# 
# # plot(x, rowSums(res$t_series) )
# # plot(x, y)
# 
# t_series <- res$t_series
# 
# plot(x, t_series[, 1])
# 
# for (i in 1:dim(res$t_series)[2]){
#   plot(x, res$t_series[, i])
# }

```

```{r}
# Ft %*% sweep(Ft_inv, 1, X[, 1], '*')[2, ]
```

```{r}
reconstruct_fft <- function(x, y, frequencies) {
  # Выполняем быстрое преобразование Фурье
  fft_y <- fft(y)

  # Получаем амплитуды и фазы
  amplitudes <- Mod(fft_y)
  phases <- Arg(fft_y)
  
  reconstructed <- matrix(0, length(amplitudes), length(x))
  n <- length(amplitudes)
  for (i in 1:(length(amplitudes))) {
    # print(i)
    reconstructed[i, ] <-
      amplitudes[i] * 
      cos(2 * pi * frequencies[i] * (x) + phases[i]) /
      n
  }
  # plot(x, reconstructed[9, ], main = paste(x[1]), type = "l", col = "red")
  # lines(x, y/2)
  # plot(x, reconstructed[L+2-9, ], main = paste(x[1]))
  return(reconstructed)
}


n <- 96*2-1
x <- 0:(n-1)
L <- 48
frequencies <- (0:(L-1)) / L
y <- sin(2*pi/12 * x)
y_main <- y
x_main <- x

X <- hankel(y, L)
K <- dim(X)[2]
res <- list()
for (i in 1:K){
  y <- X[, i]
  x <- x_main[1:(1 + L - 1)]
  res[[i]] <- reconstruct_fft(x, y, frequencies)
}

# for (i in 1:L){
#   plot(x, res[[i]][9, ])
# }

res_mult <- res
# res

averaging <- function(res_comp_wise_mult){
  K <- dim(X)[2]
  counters <- rep(0, n)
  res <- matrix(0, ncol = n, nrow = L)
  for (i in 1:length(res_comp_wise_mult)){
    res[, i:(i+L-1)] <- res[, i:(i+L-1)] + res_comp_wise_mult[[i]]
    counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
  }
  for (i in 1:n){
    res[, i] <- res[, i] / counters[i]
  }
  res
}

avr <- averaging(res_mult)

group_by_elementary_freq_foureir <- function(res_averaged){
  nf2 <- 0
  if (L %% 2) {
    nf2 <- (L + 1) / 2 - 1
  } else {
    nf2 <- L / 2 - 1
  }
  nft <- nf2 + abs((L %% 2) - 2)
  
  Z <- matrix(0, ncol = nft, nrow = n)
  
  # print(Z |> dim())
  # print(res_averaged |> dim())
  
  Z[, 1] <- res_averaged[1, ]
  for (k in 1:nf2) {
    Z[, k + 1] <- res_averaged[k + 1, ] + res_averaged[L + 2 - (k + 1), ]
  }
  if (L %% 2 != 0) {
    Z[, nft] <- res_averaged[nft, ]
  }
  
  
  return(list(
    t_series = Z,
    freq = (0:dim(Z)[2])/L
  ))
}


rs <- group_by_elementary_freq_foureir(avr)

plot(x_main, rs$t_series[, 5])

```

#### IP_values

```{r}
data_slice <- 1:537
dates_slice <- dates[data_slice]
IP_values_slice <- IP_values[data_slice]
eps <- 1/193


c <- circulant_SSA(IP_values_slice, L = 192, extend_flag = FALSE)
r <- c$t_series






reconstruct_fft <- function(x, y, frequencies) {
  # Выполняем быстрое преобразование Фурье
  fft_y <- fft(y)

  # Получаем амплитуды и фазы
  amplitudes <- Mod(fft_y)
  phases <- Arg(fft_y)
  
  reconstructed <- matrix(0, length(amplitudes), length(x))
  n <- length(amplitudes)
  for (i in 1:(length(amplitudes))) {
    # print(i)
    reconstructed[i, ] <-
      amplitudes[i] * 
      cos(2 * pi * frequencies[i] * (x) + phases[i]) /
      n
  }
  # plot(x, reconstructed[9, ], main = paste(x[1]), type = "l", col = "red")
  # lines(x, y/2)
  # plot(x, reconstructed[L+2-9, ], main = paste(x[1]))
  return(reconstructed)
}


n <- 537
x <- 0:(n-1)
L <- 192
frequencies <- (0:(L-1)) / L
y <- IP_values_slice
y_main <- y
x_main <- x

X <- hankel(y, L)
K <- dim(X)[2]
res <- list()
for (i in 1:K){
  y <- X[, i]
  x <- x_main[1:(1 + L - 1)]
  res[[i]] <- reconstruct_fft(x, y, frequencies)
}

# for (i in 1:L){
#   plot(x, res[[i]][9, ])
# }

res_mult <- res
# res

averaging <- function(res_comp_wise_mult){
  K <- dim(X)[2]
  counters <- rep(0, n)
  res <- matrix(0, ncol = n, nrow = L)
  for (i in 1:length(res_comp_wise_mult)){
    res[, i:(i+L-1)] <- res[, i:(i+L-1)] + res_comp_wise_mult[[i]]
    counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
  }
  for (i in 1:n){
    res[, i] <- res[, i] / counters[i]
  }
  res
}

avr <- averaging(res_mult)

group_by_elementary_freq_foureir <- function(res_averaged){
  nf2 <- 0
  if (L %% 2) {
    nf2 <- (L + 1) / 2 - 1
  } else {
    nf2 <- L / 2 - 1
  }
  nft <- nf2 + abs((L %% 2) - 2)
  
  Z <- matrix(0, ncol = nft, nrow = n)
  
  # print(Z |> dim())
  # print(res_averaged |> dim())
  
  Z[, 1] <- res_averaged[1, ]
  for (k in 1:nf2) {
    Z[, k + 1] <- res_averaged[k + 1, ] + res_averaged[L + 2 - (k + 1), ]
  }
  if (L %% 2 != 0) {
    Z[, nft] <- res_averaged[nft, ]
  }
  
  
  return(list(
    t_series = Z,
    freq = (0:dim(Z)[2])/L
  ))
}


rs <- group_by_elementary_freq_foureir(avr)

# plot(x_main, rs$t_series[, 5])


for (i in 1:dim(r)[2]){
  plot(1:n, rs$t_series[, i], col= "red", type = "l")
  lines(1:n, r[, i])
}


```

```{r}
cissa_like_fourier_transform <- function(ts, L){
  reconstruct_fft <- function(x, y, frequencies) {
    # Выполняем быстрое преобразование Фурье
    fft_y <- fft(y)
  
    # Получаем амплитуды и фазы
    amplitudes <- Mod(fft_y)
    phases <- Arg(fft_y)
    
    reconstructed <- matrix(0, length(amplitudes), length(x))
    n <- length(amplitudes)
    for (i in 1:(length(amplitudes))) {
      # print(i)
      reconstructed[i, ] <-
        amplitudes[i] * 
        cos(2 * pi * frequencies[i] * (x) + phases[i]) /
        n
    }
    # plot(x, reconstructed[9, ], main = paste(x[1]), type = "l", col = "red")
    # lines(x, y/2)
    # plot(x, reconstructed[L+2-9, ], main = paste(x[1]))
    return(reconstructed)
  }
  
  
  n <- length(ts)
  x <- 0:(n-1)
  L <- L
  frequencies <- (0:(L-1)) / L
  y <- ts
  y_main <- y
  x_main <- x
  
  X <- hankel(y, L)
  K <- dim(X)[2]
  res <- list()
  for (i in 1:K){
    y <- X[, i]
    x <- x_main[1:(1 + L - 1)]
    res[[i]] <- reconstruct_fft(x, y, frequencies)
  }
  
  # for (i in 1:L){
  #   plot(x, res[[i]][9, ])
  # }
  
  res_mult <- res
  # res
  
  averaging <- function(res_comp_wise_mult){
    K <- dim(X)[2]
    counters <- rep(0, n)
    res <- matrix(0, ncol = n, nrow = L)
    for (i in 1:length(res_comp_wise_mult)){
      res[, i:(i+L-1)] <- res[, i:(i+L-1)] + res_comp_wise_mult[[i]]
      counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
    }
    for (i in 1:n){
      res[, i] <- res[, i] / counters[i]
    }
    res
  }
  
  avr <- averaging(res_mult)
  
  group_by_elementary_freq_foureir <- function(res_averaged){
    nf2 <- 0
    if (L %% 2) {
      nf2 <- (L + 1) / 2 - 1
    } else {
      nf2 <- L / 2 - 1
    }
    nft <- nf2 + abs((L %% 2) - 2)
    
    Z <- matrix(0, ncol = nft, nrow = n)
    
    # print(Z |> dim())
    # print(res_averaged |> dim())
    
    Z[, 1] <- res_averaged[1, ]
    for (k in 1:nf2) {
      Z[, k + 1] <- res_averaged[k + 1, ] + res_averaged[L + 2 - (k + 1), ]
    }
    if (L %% 2 != 0) {
      Z[, nft] <- res_averaged[nft, ]
    }
    
    
    return(list(
      t_series = Z,
      freq = (0:dim(Z)[2])/L
    ))
  }


  rs <- group_by_elementary_freq_foureir(avr)
  return(rs)
}

```

```{r}
data_slice <- 1:537
dates_slice <- dates[data_slice]
IP_values_slice <- IP_values[data_slice]
eps <- 1/193


c <- circulant_SSA(IP_values_slice, L = 192, extend_flag = FALSE)
r <- c$t_series

c_ft <- cissa_like_fourier_transform(IP_values_slice, L = 192)
r_ft <- c_ft$t_series


for (i in 1:dim(r)[2]){
  plot(1:n, r_ft[, i], col= "red", type = "l", lwd = 2)
  lines(1:n, r[, i])
}
```
